Chapter 5 Resource Masters - Math Problem Solvingjaeproblemsolving.weebly.com/uploads/5/1/9/6/51966985/...©Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using the

Chapter 5Resource Masters

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ISBN: 0-07-827729-9 Glencoe Algebra 1Chapter 5 Resource Masters

3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04

Glencoe/McGraw-Hill

CONSUMABLE WORKBOOKS Many of the worksheets contained in the ChapterResource Masters booklets are available as consumable workbooks in bothEnglish and Spanish.

Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7Reading to Learn Mathematics Workbook 0-07-861060-5

ANSWERS FOR WORKBOOKS The answers for Chapter 5 of these workbookscan be found in the back of this Chapter Resource Masters booklet.

StudentWorks™ This CD-ROM includes the entire Student Edition text alongwith the English workbooks listed above.

TeacherWorks™ All of the materials found in this booklet are included for view-ing and printing in the Glencoe Algebra 1 TeacherWorks CD-ROM.

© Glencoe/McGraw-Hill iii Glencoe Algebra 1

Contents

Vocabulary Builder . . . . . . . . . . . . . . . . vii

Lesson 5-1Study Guide and Intervention . . . . . . . . 281–282Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 283Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 284Reading to Learn Mathematics . . . . . . . . . . 285Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 286







Chapter 5 AssessmentChapter 5 Test, Form 1 . . . . . . . . . . . . 323–324Chapter 5 Test, Form 2A . . . . . . . . . . . 325–326Chapter 5 Test, Form 2B . . . . . . . . . . . 327–328Chapter 5 Test, Form 2C . . . . . . . . . . . 329–330Chapter 5 Test, Form 2D . . . . . . . . . . . 331–332Chapter 5 Test, Form 3 . . . . . . . . . . . . 333–334Chapter 5 Open-Ended Assessment . . . . . . 335Chapter 5 Vocabulary Test/Review . . . . . . . 336Chapter 5 Quizzes 1 & 2 . . . . . . . . . . . . . . . 337Chapter 5 Quizzes 3 & 4 . . . . . . . . . . . . . . . 338Chapter 5 Mid-Chapter Test . . . . . . . . . . . . . 339Chapter 5 Cumulative Review . . . . . . . . . . . 340Chapter 5 Standardized Test Practice . . 341–342

Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1

ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A32

© Glencoe/McGraw-Hill iv Glencoe Algebra 1

Teacher’s Guide to Using theChapter 5 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 5 Resource Masters includes the core materials neededfor Chapter 5. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.

Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.

WHEN TO USE Give these pages tostudents before beginning Lesson 5-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.

Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.

WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.

Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.

WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.

Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.

WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.

WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.

Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.

WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.

© Glencoe/McGraw-Hill v Glencoe Algebra 1

Assessment OptionsThe assessment masters in the Chapter 5Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.

Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions

and is intended for use with basic levelstudents.

• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.

• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.

All of the above tests include a free-response Bonus question.

• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.

• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.

Intermediate Assessment• Four free-response quizzes are included

to offer assessment at appropriateintervals in the chapter.

• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.

Continuing Assessment• The Cumulative Review provides

students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.

• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questionsthat appear in the Student Edition onpages 314–315. This improves students’familiarity with the answer formats theymay encounter in test taking.

• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.

• Full-size answer keys are provided forthe assessment masters in this booklet.

Reading to Learn MathematicsVocabulary Builder

NAME ______________________________________________ DATE ____________ PERIOD _____

55

© Glencoe/McGraw-Hill vii Glencoe Algebra 1

Voca

bula

ry B

uild

erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 5.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.

Vocabulary Term Found on Page Definition/Description/Example

constant of variation

direct variation

family of graphs

line of fit

linear extrapolation

ihk·STRA·puh·LAY·shun

linear interpolation

ihn·TUHR·puh·LAY·shun

negative correlation

KAWR·uh·LAY·shun

parallel lines

(continued on the next page)

© Glencoe/McGraw-Hill viii Glencoe Algebra 1

Vocabulary Term Found on Page Definition/Description/Example

perpendicular lines

PUHR·puhn·DIH·kyuh·luhr

point-slope form

positive correlation

rate of change

scatter plot

slope

slope-intercept form

IHN·tuhr·SEHPT

Reading to Learn MathematicsVocabulary Builder (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

55

Study Guide and InterventionSlope

NAME ______________________________________________ DATE ____________ PERIOD _____

5-15-1

© Glencoe/McGraw-Hill 281 Glencoe Algebra 1

Less

on

5-1

Find Slope

Slope of a Linem � or m � , where (x1, y1) and (x2, y2) are the coordinates

of any two points on a nonvertical line

y2 � y1�x2 � x1

rise�run

Find the slope of theline that passes through (�3, 5)and (4, �2).

Let (�3, 5) � (x1, y1) and (4, �2) � (x2, y2).

m � Slope formula

� y2 � �2, y1 � 5, x2 � 4, x1 � �3

� Simplify.

� �1

�7�7

�2 � 5��4 � (�3)

y2 � y1�x2 � x1

Find the value of r so that the line through (10, r) and (3, 4) has a

slope of � .

m � Slope formula

� � m � � , y2 � 4, y1 � r, x2 � 3, x1 � 10

� � Simplify.

�2(�7) � 7(4 � r) Cross multiply.

14 � 28 � 7r Distributive Property

�14 � �7r Subtract 28 from each side.

2 � r Divide each side by �7.

4 � r�

�72�7

2�7

4 � r�3 � 10

2�7

y2 � y1�x2 � x1

2�7

Example 1Example 1 Example 2Example 2

ExercisesExercises

Find the slope of the line that passes through each pair of points.

1. (4, 9), (1, 6) 2. (�4, �1), (�2, �5) 3. (�4, �1), (�4, �5)

4. (2, 1), (8, 9) 5. (14, �8), (7, �6) 6. (4, �3), (8, �3)

7. (1, �2), (6, 2) 8. (2, 5), (6, 2) 9. (4, 3.5), (�4, 3.5)

Determine the value of r so the line that passes through each pair of points hasthe given slope.

10. (6, 8), (r, �2), m � 1 11. (�1, �3), (7, r), m � 12. (2, 8), (r, �4) m � �3

13. (7, �5), (6, r), m � 0 14. (r, 4), (7, 1), m � 15. (7, 5), (r, 9), m � 6

16. (10, r), (3, 4), m � � 17. (10, 4), (�2, r), m � �0.5 18. (r, 3), (7, r), m � �1�5

2�7

3�4

3�4


Rate of Change The rate of change tells, on average, how a quantity is changing overtime. Slope describes a rate of change.

POPULATION The graph shows the population growth in China.

a. Find the rates of change for 1950–1975 and for 1975–2000.

1950–1975: �

� or 0.0152

1975–2000: �

� or 0.0124

b. Explain the meaning of the slope in each case.From 1950–1975, the growth was 0.0152 billion per year, or 15.2 million per year.From 1975–2000, the growth was 0.0124 billion per year, or 12.4 million per year.

c. How are the different rates of change shown on the graph?There is a greater vertical change for 1950–1975 than for 1975–2000. Therefore, thesection of the graph for 1950–1975 has a steeper slope.

LONGEVITY The graph shows the predicted life expectancy for men and women born in a given year.

1. Find the rates of change for women from 2000–2025 and 2025–2050.

2. Find the rates of change for men from 2000–2025 and2025–2050.

3. Explain the meaning of your results in Exercises 1 and 2.

4. What pattern do you see in the increase with each 25-year period?

5. Make a prediction for the life expectancy for 2050–2075. Explain how you arrived atyour prediction.

Predicting Life Expectancy

Year Born

Ag

e

2000

WomenMen

100

95

90

85

80

75

70

65

2050*2025*

*Estimated

Source: USA TODAY

8084

8178

74

87

0.31�25

1.24 � 0.93��2000 � 1975

change in population��change in time

0.38�25

0.93 � 0.55��1975 � 1950

change in population��change in time

Population Growth in China

Year

Peo

ple

(b

illio

ns)

1950 1975 2000

2.0

1.5

1.0

0.5

02025*

*Estimated

Source: United Nations Population Division

0.550.93

1.241.48

Study Guide and Intervention (continued)

Slope

NAME ______________________________________________ DATE ____________ PERIOD _____

5-15-1

ExercisesExercises

ExampleExample

Skills PracticeSlope

NAME ______________________________________________ DATE ____________ PERIOD _____

5-15-1


Less

on

5-1


1. 2. 3.

4. (2, 5), (3, 6) 5. (6, 1), (�6, 1)

6. (4, 6), (4, 8) 7. (5, 2), (5, �2)

8. (2, 5), (�3, �5) 9. (9, 8), (7, �8)

10. (�5, �8), (�8, 1) 11. (�3, 10), (�3, 7)

12. (17, 18), (18, 17) 13. (�6, �4), (4, 1)

14. (10, 0), (�2, 4) 15. (2, �1), (�8, �2)

16. (5, �9), (3, �2) 17. (12, 6), (3, �5)

18. (�4, 5), (�8, �5) 19. (�5, 6), (7, �8)

Find the value of r so the line that passes through each pair of points has thegiven slope.

20. (r, 3), (5, 9), m � 2 21. (5, 9), (r, �3), m � �4

22. (r, 2), (6, 3), m � 23. (r, 4), (7, 1), m �

24. (5, 3), (r, �5), m � 4 25. (7, r), (4, 6), m � 0

3�4

1�2

(0, 1)

(1, –2)x

y

O

(0, 0)

(3, 1)

x

y

O(0, 1)

(2, 5)

x

y

O



1. 2. 3.

4. (6, 3), (7, �4) 5. (�9, �3), (�7, �5)

6. (6, �2), (5, �4) 7. (7, �4), (4, 8)

8. (�7, 8), (�7, 5) 9. (5, 9), (3, 9)

10. (15, 2), (�6, 5) 11. (3, 9), (�2, 8)

12. (�2, �5), (7, 8) 13. (12, 10), (12, 5)

14. (0.2, �0.9), (0.5, �0.9) 15. � , �, �� , �

Find the value of r so the line that passes through each pair of points has thegiven slope.

16. (�2, r), (6, 7), m � 17. (�4, 3), (r, 5), m �

18. (�3, �4), (�5, r), m � � 19. (�5, r), (1, 3), m �

20. (1, 4), (r, 5), m undefined 21. (�7, 2), (�8, r), m � �5

22. (r, 7), (11, 8), m � � 23. (r, 2), (5, r), m � 0

24. ROOFING The pitch of a roof is the number of feet the roof rises for each 12 feethorizontally. If a roof has a pitch of 8, what is its slope expressed as a positive number?

25. SALES A daily newspaper had 12,125 subscribers when it began publication. Five yearslater it had 10,100 subscribers. What is the average yearly rate of change in the numberof subscribers for the five-year period?

1�5

7�6

9�2

1�4

1�2

2�3

1�3

4�3

7�3

(–2, 3)(3, 3)

x

y

O

(3, 1)

(–2, –3)

x

y

O(–1, 0)

(–2, 3)

x

y

O

Practice Slope

NAME ______________________________________________ DATE ____________ PERIOD _____

5-15-1

Reading to Learn MathematicsSlope

NAME ______________________________________________ DATE______________ PERIOD _____

5-15-1


Less

on

5-1

Pre-Activity Why is slope important in architecture?

Read the introduction to Lesson 5-1 at the top of page 256 in your textbook. Then complete the definition of slope and fill in the boxeson the graph with the words rise and run.

slope �

In this graph, the rise is units, and the run is units.

Thus, the slope of this line is or .

Reading the Lesson1. Describe each type of slope and include a sketch.

Type of Slope Description of Graph Sketch

positive The graph rises as you go from left to right.

negative The graph falls as you go from left to right.

zero The graph is a horizontal line.

undefined The graph is a vertical line.

2. Describe how each expression is related to slope.

a. difference of y-coordinates divided by difference ofcorresponding x-coordinates

b. how far up or down as compared to how far left or right

c. slope used as rate of change

Helping You Remember3. The word rise is usually associated with going up. Sometimes going from one point on

the graph does not involve a rise and a run but a fall and a run. Describe how you couldselect points so that it is always a rise from the first point to the second point.Sample answer: If the slope is negative, choose the second point so that its x-coordinate is less than that of the first point.

$52,000 increase in spending��26 months

rise�run

y2 � y1�x2 � x1

3�5

3 units�5 units

53

rise�run

x

y

O


Treasure Hunt with SlopesUsing the definition of slope, draw lines with the slopes listed below. A correct solution will trace the route to the treasure.

1. 3 2. 3. � 4. 0

5. 1 6. �1 7. no slope 8.

9. 10. 11. � 12. 33�4

1�3

3�2

2�7

2�5

1�4

Start Here

Treasure

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

5-15-1

Study Guide and InterventionSlope and Direct Variation

NAME ______________________________________________ DATE ____________ PERIOD _____

5-25-2


Less

on

5-2

Direct Variation A direct variation is described by an equation of the form y � kx,where k � 0. We say that y varies directly as x. In the equation y � kx, k is the constant of variation.

Name the constant ofvariation for the equation. Then findthe slope of the line that passesthrough the pair of points.

For y � x, the constant of variation is .

m � Slope formula

� (x1, y1) � (0, 0), (x2, y2) � (2, 1)

� Simplify.

The slope is .1�2

1�2

1 � 0�2 � 0

y2 � y1�x2 � x1

1�2

1�2

(2, 1)(0, 0) x

y

Oy � 12x

Suppose y variesdirectly as x, and y � 30 when x � 5.

a. Write a direct variation equationthat relates x and y.Find the value of k.

y � kx Direct variation equation

30 � k(5) Replace y with 30 and x with 5.

6 � k Divide each side by 5.

Therefore, the equation is y � 6x.

b. Use the direct variation equation tofind x when y � 18.

y � 6x Direct variation equation

18 � 6x Replace y with 18.

3 � x Divide each side by 6.

Therefore, x � 3 when y � 18.


ExercisesExercises

Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.

1. 2. 3.

Write a direct variation equation that relates x to y. Assume that y varies directlyas x. Then solve.

4. If y � 4 when x � 2, find y when x � 16.

5. If y � 9 when x � �3, find x when y � 6.

6. If y � �4.8 when x � �1.6, find x when y � �24.

7. If y � when x � , find x when y � .3

�161�8

1�4

(–2, –3)

(0, 0)x

y

O

y � 32x

(1, 3)

(0, 0) x

y

O

y � 3x(–1, 2)

(0, 0)x

y

Oy � –2x


Solve Problems The distance formula d � rt is a direct variation equation. In theformula, distance d varies directly as time t, and the rate r is the constant of variation.

TRAVEL A family drove their car 225 miles in 5 hours.

a. Write a direct variation equation to find the distance traveled for any numberof hours.Use given values for d and t to find r.

d � rt Original equation

225 � r(5) d � 225 and t � 5

45 � r Divide each side by 5.

Therefore, the direct variation equation is d � 45t.b. Graph the equation.

The graph of d � 45t passes through the origin withslope 45.

m �

✓CHECK (5, 225) lies on the graph.c. Estimate how many hours it would take the

family to drive 360 miles.d � 45t Original equation

360 � 45t Replace d with 360.

t � 8 Divide each side by 45.

Therefore, it will take 8 hours to drive 360 miles.

RETAIL The total cost C of bulk jelly beans is $4.49 times the number of pounds p.

1. Write a direct variation equation that relates the variables.

2. Graph the equation on the grid at the right.

3. Find the cost of pound of jelly beans.

CHEMISTRY Charles’s Law states that, at a constant pressure, volume of a gas V varies directly as its temperatureT. A volume of 4 cubic feet of a certain gas has a temperatureof 200° (absolute temperature).

4. Write a direct variation equation that relates the variables.


6. Find the volume of the same gas at 250° (absolute temperature).

Charles’s Law

Temperature (�K)

Vo

lum

e (c

ub

ic f

eet)

1000 200 T

V

4

3

2

1

3�4

Cost of Jelly Beans

Weight (pounds)

Co

st (

do

llars

)

20 4 w

C

18.00

13.50

9.00

4.50

rise�run

45�1

Automobile Trips

Time (hours)

Dis

tan

ce (

mile

s)10 2 3 4 5 6 7 8 t

d

360

270

180

90(1, 45)

(5, 225)d � 45t


Slope and Direct Variation

NAME ______________________________________________ DATE ____________ PERIOD _____

5-25-2

ExampleExample

ExercisesExercises

Skills PracticeSlope and Direct Variation

NAME ______________________________________________ DATE ____________ PERIOD _____

5-25-2


Less

on

5-2


1. 2. 3.

Graph each equation.

4. y � 3x 5. y � � x 6. y � x

Write a direct variation equation that relates x and y. Assume that y variesdirectly as x. Then solve.

7. If y � �8 when x � �2, find x 8. If y � 45 when x � 15, find xwhen y � 32. when y � 15.

9. If y � �4 when x � 2, find y 10. If y � �9 when x � 3, find ywhen x � �6. when x � �5.

11. If y � 4 when x � 16, find y 12. If y � 12 when x � 18, find xwhen x � 6. when y � �16.

Write a direct variation equation that relates the variables. Then graph theequation.

13. TRAVEL The total cost C of gasoline 14. SHIPPING The number of delivered toys Tis $1.80 times the number of gallons g. is 3 times the total number of crates c.

Toys Shipped

Crates

Toys

20 4 6 71 3 5 c

T

21

18

15

12

9

6

3

Gasoline Cost

Gallons

Co

st (

$)

40 8 12 142 6 10 g

C

28

24

20

16

12

8

4

x

y

O

2�5

x

y

O

3�4

x

y

O

(–2, 3)

(0, 0)x

y

O

y � – 32x

(–1, 2)(0, 0)

x

y

O

y � –2x

(3, 1)(0, 0)

x

y

O

y � 13x



1. ; 2. ; 3. � ;�


4. y � �2x 5. y � x 6. y � � x

Write a direct variation equation that relates x and y. Assume that y variesdirectly as x. Then solve.

7. If y � 7.5 when x � 0.5, find y when x � �0.3. y � 15x; �4.5

8. If y � 80 when x � 32, find x when y � 100. y � 2.5x; 40

9. If y � when x � 24, find y when x � 12. y � x;

Write a direct variation equation that relates the variables. Then graph theequation.

10. MEASURE The width W of a 11. TICKETS The total cost C of tickets isrectangle is two thirds of the length �. $4.50 times the number of tickets t.

W � � C � 4.50t

12. PRODUCE The cost of bananas varies directly with their weight. Miguel bought

3 pounds of bananas for $1.12. Write an equation that relates the cost of the bananas

to their weight. Then find the cost of 4 pounds of bananas. C � 0.32p; $1.361�4

1�2

Rectangle Dimensions

Length

Wid

th

40 8 122 6 10 �

W

10

8

6

4

2

2�3

3�8

1�32

3�4

5�3

x

y

O

6�5

x

y

O

5�2

5�2

(–2, 5)

(0, 0)x

y

O

y � � 52x

4�3

4�3(3, 4)

(0, 0)x

y

O

y � 43x

3�4

3�4

(4, 3)

(0, 0)x

y

O

y � 34x

Practice (Average)

Slope and Direct Variation

NAME ______________________________________________ DATE______________ PERIOD _____

5-25-2

Reading to Learn MathematicsSlope and Direct Variation

NAME ______________________________________________ DATE______________ PERIOD _____

5-25-2


Less

on

5-2

Pre-Activity How is slope related to your shower?

Read the introduction to Lesson 5-2 at the top of page 264 in your textbook.

• How do the numbers in the table relate to the graph shown?They are the coordinates of the points on the graph.

• Think about the first sentence. What does it mean to say that a standardshowerhead uses about 6 gallons of water per minute?Sample answer: For each minute the shower runs, 6 gallonsof water come out. So, if the shower ran 10 minutes, thatwould be 60 gallons.

Reading the Lesson

1. What is the form of a direct variation equation? y � kx

2. How is the constant of variation related to slope? The constant of variation hasthe same value as the slope of the graph of the equation.

3. The expression “y varies directly as x” can be written as the equation y � kx. How wouldyou write an equation for “w varies directly as the square of t”? w � kt2

4. For each situation, write an equation with the proper constant of variation.

a. The distance d varies directly as time t, and a cheetah can travel 88 feet in 1 second.d � 88t

b. The perimeter p of a pentagon with all sides of equal length varies directly as thelength s of a side of the pentagon. A pentagon has 5 sides. p � 5s

c. The wages W earned by an employee vary directly with the number of hours h thatare worked. Enrique earned $172.50 for 23 hours of work. W � $7.50h

Helping You Remember

5. Look up the word constant in a dictionary. How does this definition relate to the termconstant of variation? Sample answer: Something unchanging; the constantof variation relates x and y in the same value every time, and thatrelationship never changes.


nth Power VariationAn equation of the form y � kxn, where k � 0, describes an nth powervariation. The variable n can be replaced by 2 to indicate the second powerof x (the square of x) or by 3 to indicate the third power of x (the cube of x).

Assume that the weight of a person of average build varies directly as thecube of that person’s height. The equation of variation has the form w � kh3.

The weight that a person’s legs will support is proportional to the cross-sectional area of the leg bones. This area varies directly as the squareof the person’s height. The equation of variation has the form s � kh2.

Answer each question.

1. For a person 6 feet tall who weighs 200 pounds, find a value for k in the equation w � kh3.

2. Use your answer from Exercise 1 to predict the weight of a person who is 5 feet tall.

3. Find the value for k in the equation w � kh3 for a baby who is 20 inches long and weighs 6 pounds.

4. How does your answer to Exercise 3 demonstrate that a baby is significantly fatter in proportion to its height than an adult?

5. For a person 6 feet tall who weighs 200 pounds, find a value for k in the equation s � kh2.

6. For a baby who is 20 inches long and weighs 6 pounds, find an “infant value” for k in the equation s � kh2.

7. According to the adult equation you found (Exercise 1), how much would an imaginary giant 20 feet tall weigh?

8. According to the adult equation for weight supported (Exercise 5), how much weight could a 20-foot tall giant’s legs actually support?

9. What can you conclude from Exercises 7 and 8?

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

5-25-2

Study Guide and InterventionSlope-Intercept Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-35-3


Less

on

5-3

Slope-Intercept Form

Slope-Intercept Form y � mx � b, where m is the given slope and b is the y-intercept

Write an equation of the line whose slope is �4 and whose y-intercept is 3.y � mx � b Slope-intercept form

y � �4x � 3 Replace m with �4 and b with 3.

Graph 3x � 4y � 8.

3x � 4y � 8 Original equation

�4y � �3x � 8 Subtract 3x from each side.

� Divide each side by �4.

y � x � 2 Simplify.

The y-intercept of y � x � 2 is �2 and the slope is . So graph the point (0, �2). From

this point, move up 3 units and right 4 units. Draw a line passing through both points.

Write an equation of the line with the given slope and y-intercept.

1. slope: 8, y-intercept �3 2. slope: �2, y-intercept �1 3. slope: �1, y-intercept �7

Write an equation of the line shown in each graph.

4. 5. 6.


7. y � 2x � 1 8. y � �3x � 2 9. y � �x � 1

x

y

Ox

y

Ox

y

O

(4, –2)

(0, –5)

xy

O

(3, 0)

(0, 3)

x

y

O(0, –2)

(1, 0) x

y

O

3�4

3�4

3�4

�3x � 8��

�4�4y��4

(0, –2)

(4, 1)

x

y

O

3x � 4y � 8

Example 1Example 1

Example 2Example 2

ExercisesExercises


Model Real-World Data

MEDIA Since 1997, the number of cable TV systems has decreasedby an average rate of 121 systems per year. There were 10,943 systems in 1997.

a. Write a linear equation to find the average number of cable systems in any yearafter 1997.The rate of change is �121 systems per year. In the first year, the number of systems was10,943. Let N � the number of cable TV systems. Let x � the number of years after 1997.An equation is N � �121x � 10,943.

b. Graph the equation.The graph of N � �121x � 10,943 is a line that passesthrough the point at (0, 10,943) and has a slope of �121.

c. Find the approximate number of cable TV systems in 2000.N � �121x � 10,943 Original equation

N � �121(3) � 10,943 Replace x with 3.

N � 10,580 Simplify.

There were about 10,580 cable TV systems in 2000.

ENTERTAINMENT In 1995, 65.7% of all households with TV’s in the U.S. subscribed to cable TV. Between 1995and 1999, the percent increased by about 0.6% each year.

1. Write an equation to find the percent P of households thatsubscribed to cable TV for any year x between 1995 and 1999.


3. Find the percent that subscribed to cable TV in 1999.

POPULATION The population of the United States is projected to be 300 million by the year 2010. Between 2010 and 2050, the population is expected to increase byabout 2.5 million per year.

4. Write an equation to find the population P in any year xbetween 2010 and 2050.


6. Find the population in 2050.

Projected UnitedStates Population

Years Since 2010

Pop

ula

tio

n (

mill

ion

s)

0 20 40 x

P

400

380

360

340

320

300

Source: The World Almanac

Percent of Householdswith TV Having Cable

Years Since 1995

Perc

ent

10 2 3 4 5 x

P

68

67

66

65


Cable TV Systems

Years Since 1997

Nu

mb

er o

f C

able

TV

Sys

tem

s

10 2 3 4 5 6 x

N

10,900

10,800

10,700

10,600

10,500




NAME ______________________________________________ DATE ____________ PERIOD _____

5-35-3

ExampleExample

ExercisesExercises

Skills PracticeSlope-Intercept Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-35-3


Less

on

5-3


1. slope: 5, y-intercept: �3 2. slope: �2, y-intercept: 7

3. slope: �6, y-intercept: �2 4. slope: 7, y-intercept: 1

5. slope: 3, y-intercept: 2 6. slope: �4, y-intercept: �9

7. slope: 1, y-intercept: �12 8. slope: 0, y-intercept: 8


9. 10. 11.


12. y � x � 4 13. y � �2x � 1 14. x � y � �3

Write a linear equation in slope-intercept form to model each situation.

15. A video store charges $10 for a rental card plus $2 per rental.

16. A Norfolk pine is 18 inches tall and grows at a rate of 1.5 feet per year.

17. A Cairn terrier weighs 30 pounds and is on a special diet to lose 2 pounds per month.

18. An airplane at an altitude of 3000 feet descends at a rate of 500 feet per mile.

x

y

O

x

y

Ox

y

O

(0, –1)(2, –3)

x

y

O

(0, 2)

(2, –4)

x

y

O(2, 1)

(0, –3)

x

y

O



1. slope: , y-intercept: 3 2. slope: , y-intercept: �4

3. slope: 1.5, y-intercept: �1 4. slope: �2.5, y-intercept: 3.5


5. 6. 7.


8. y � � x � 2 9. 3y � 2x � 6 10. 6x � 3y � 6

Write a linear equation in slope-intercept form to model each situation.

11. A computer technician charges $75 for a consultation plus $35 per hour.

12. The population of Pine Bluff is 6791 and is decreasing at the rate of 7 per year.

WRITING For Exercises 13–15, use the following information.Carla has already written 10 pages of a novel. She plansto write 15 additional pages per month until she is finished.

13. Write an equation to find the total number of pages Pwritten after any number of months m.


15. Find the total number of pages written after 5 months.

Carla’s Novel

Months

Pag

es W

ritt

en

20 4 61 3 5 m

P

100

80

60

40

20

x

y

Ox

y

O

1�2

(–3, 0)

(0, –2)

x

y

O(–2, 0)

(0, 3)

x

y

O(–5, 0)

(0, 2)

x

y

O

3�2

1�4

Practice Slope-Intercept Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-35-3

Reading to Learn MathematicsSlope-Intercept Form

NAME ______________________________________________ DATE______________ PERIOD _____

5-35-3


Less

on

5-3

Pre-Activity How is a y-intercept related to a flat fee?


• What point on the graph shows that the flat fee is $5.00?

• How does the rate of $0.10 per minute relate to the graph?

Reading the Lesson

1. Fill in the boxes with the correct words to describe what m and b represent.

y � mx � b↑ ↑

2. What are the slope and y-intercept of a vertical line?

The slope is undefined, and there is no y-intercept.

3. What are the slope and y-intercept of a horizontal line?

The slope is 0, and the y-intercept is where it crosses the y-axis.

4. Read the problem. Then answer each part of the exercise.

A ruby-throated hummingbird weighs about 0.6 gram at birth and gains weight at a rateof about 0.2 gram per day until fully grown.

a. Write a verbal equation to show how the words are related to finding the averageweight of a ruby-throated hummingbird at any given week. Use the words weight atbirth, rate of growth, weight, and weeks after birth. Below the equation, fill in anyvalues you know and put a question mark under the items that you do not know.

� � �

b. Define what variables to use for the unknown quantities.

c. Use the variables you defined and what you know from the problem to write anequation.


5. One way to remember something is to explain it to another person. Write how you wouldexplain to someone the process for using the y-intercept and slope to graph a linearequation.

weight?

rate of growth0.2

weeks after birth?

weight at birth0.6


Relating Slope-Intercept Form and Standard Forms

You have learned that slope can be defined in terms of or .

Another definition can be found from the standard from of a linear equation. Standard form is Ax � By � C, where A, B, and C are integers, A � 0, and A and B are not both zero.

1. Solve Ax � By � C for y. Your answer should be written in slope-intercept form.

2. Use the slope-intercept equation you wrote in Exercise 1 to write expressions for the slope and the y-intercept in terms of A, B, and C.

Use the expressions in Exercise 2 above to find the slope and y-intercept of each equation.

3. 2x � y � �4 4. 4x � 3y � 24

5. 4x � 6y � �36 6. x � 3y � �27

7. x � 2y � 6 8. 4y � 20

y2 � y1�x2 � x1

rise�run

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

5-35-3

Study Guide and InterventionWriting Equations in Slope-Intercept Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-45-4


Less

on

5-4

Write an Equation Given the Slope and One Point

Write an equation ofa line that passes through (�4, 2)with slope 3.

The line has slope 3. To find the y-intercept, replace m with 3 and (x, y)with (�4, 2) in the slope-intercept form.Then solve for b.

y � mx � b Slope-intercept form

2 � 3(�4) � b m � 3, y � 2, and x � �4

2 � �12 � b Multiply.

14 � b Add 12 to each side.

Therefore, the equation is y � 3x � 14.

Write an equation of the linethat passes through (�2, �1) with slope .

The line has slope . Replace m with and (x, y)

with (�2, �1) in the slope-intercept form.


�1 � (�2) � b m � , y � �1, and x � �2

�1 � � � b Multiply.

� � b Add to each side.

Therefore, the equation is y � x � .1�2

1�4

1�2

1�2

1�2

1�4

1�4

1�4

1�4

1�4


ExercisesExercises

Write an equation of the line that passes through each point with the given slope.

1. 2. 3.

4. (8, 2), m � � 5. (�1, �3), m � 5 6. (4, �5), m � �

7. (�5, 4), m � 0 8. (2, 2), m � 9. (1, �4), m � �6

10. Write an equation of a line that passes through the y-intercept �3 with slope 2.

11. Write an equation of a line that passes through the x-intercept 4 with slope �3.

12. Write an equation of a line that passes through the point (0, 350) with slope .1�5

1�2

1�2

3�4

(2, 4)

x

y

O

m � 12

(0, 0)x

y

O

m � –2

(3, 5)

x

y

O

m � 2


Write an Equation Given Two Points

Write an equation of the line that passes through (1, 2) and (3, �2).

Find the slope m. To find the y-intercept, replace m with its computed value and (x, y) with(1, 2) in the slope-intercept form. Then solve for b.

m � Slope formula

m � y2 � �2, y1 � 2, x2 � 3, x1 � 1

m � �2 Simplify.


2 � �2(1) � b Replace m with �2, y with 2, and x with 1.

2 � �2 � b Multiply.

4 � b Add 2 to each side.

Therefore, the equation is y � �2x � 4.

Write an equation of the line that passes through each pair of points.

1. 2. 3.

4. (�1, 6), (7, �10) 5. (0, 2), (1, 7) 6. (6, �25), (�1, 3)

7. (�2, �1), (2, 11) 8. (10, �1), (4, 2) 9. (�14, �2), (7, 7)

10. Write an equation of a line that passes through the x-intercept 4 and y-intercept �2.

11. Write an equation of a line that passes through the x-intercept �3 and y-intercept 5.

12. Write an equation of a line that passes through (0, 16) and (�10, 0).

(0, 1)

(–3, 0) x

y

O

(0, 4)

(4, 0) x

y

O

(1, 1)

(0, –3)

x

y

O

�2 � 2�3 �1

y2 � y1�x2 � x1


Writing Equations in Slope-Intercept Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-45-4

ExampleExample

ExercisesExercises

Skills PracticeWriting Equations in Slope-Intercept Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-45-4


Less

on

5-4


1. 2. 3.

4. (1, 9), m � 4 5. (4, 2), m � �2 6. (2, �2), m � 3

7. (3, 0), m � 5 8. (�3, �2), m � 2 9. (�5, 4), m � �4


10. 11. 12.

13. (1, 3), (�3, �5) 14. (1, 4), (6, �1) 15. (1, �1), (3, 5)

16. (�2, 4), (0, 6) 17. (3, 3), (1, �3) 18. (�1, 6), (3, �2)

Write an equation of the line that has each pair of intercepts.

19. x-intercept: �3, y-intercept: 6 20. x-intercept: 3, y-intercept: 3

21. x-intercept: 1, y-intercept: 2 22. x-intercept: 2, y-intercept: �4

23. x-intercept: �4, y-intercept: �8 24. x-intercept: �1, y-intercept: 4

(2, –1)

(0, 3)

x

y

O(–1, –3)

(1, 1)x

y

O

(–2, 3)

(3, –2)

x

y

O

(–1, 2)

x

y

O

m � 2

(4, 1)

x

y

O

m � 1

(–1, 4)

x

y

O

m � –3



1. 2. 3.

4. (�5, 4), m � �3 5. (4, 3), m � 6. (1, �5), m � �


7. 8. 9.

10. (0, �4), (5, �4) 11. (�4, �2), (4, 0) 12. (�2, �3), (4, 5)

13. (0, 1), (5, 3) 14. (�3, 0), (1, �6) 15. (1, 0), (5, �1)

Write an equation of the line that has each pair of intercepts.

16. x-intercept: 2, y-intercept: �5 17. x-intercept: 2, y-intercept: 10

18. x-intercept: �2, y-intercept: 1 19. x-intercept: �4, y-intercept: �3

20. DANCE LESSONS The cost for 7 dance lessons is $82. The cost for 11 lessons is $122.Write a linear equation to find the total cost C for � lessons. Then use the equation tofind the cost of 4 lessons.

21. WEATHER It is 76°F at the 6000-foot level of a mountain, and 49°F at the 12,000-footlevel of the mountain. Write a linear equation to find the temperature T at an elevatione on the mountain, where e is in thousands of feet.

(–3, 1)

(–1, –3)

x

y

O(0, 5)

(4, 1)x

y

O

(4, –2)

(2, –4)

xy

O

3�2

1�2

(–1, –3)

x

y

O

m � –1

(–2, 2)

x

y

O

m � –2

(1, 2)

x

y

Om � 3

Practice Writing Equations in Slope-Intercept Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-45-4

Reading to Learn MathematicsWriting Equations in Slope-Intercept Form

NAME ______________________________________________ DATE______________ PERIOD _____

5-45-4


Less

on

5-4

Pre-Activity How can slope-intercept form be used to make predictions?


• What is the rate of change per year? about 2000 per year• Study the pattern on the graph. How would you find the population in

1997? Add 2000 to the 1996 population, which gives 179,000.

Reading the Lesson

1. Suppose you are given that a line goes through (2, 5) and has a slope of �2. Use thisinformation to complete the following equation.

y � mx � b↓ ↓� � �

2. What must you first do if you are not given the slope in the problem?

Use the information given (two points) to find the slope.

3. What is the first step in answering any standardized test practice question?

Read the problem.

4. What are four steps you can use in solving a word problem?

Explore, Plan, Solve, Examine

5. Define the term linear extrapolation.

Linear extrapolation means using a linear equation to predict values thatare outside the two given data points.


6. In your own words, explain how you would answer a question that asks you to write the slope-intercept form of an equation. Sample answer: Determine whatinformation you are given. If you have a point and the slope, you cansubstitute the x- and y-values and the slope into y � mx � b to find thevalue of b. Then use the values of m and b to write the equation. If youhave two points, use them to find the slope, and then use the method fora point and the slope.

b2�25


Celsius and Kelvin TemperaturesIf you blow up a balloon and put it in the refrigerator, the balloon will shrink as the temperature of the air in the balloon decreases.

The volume of a certain gas is measured at 30° Celsius. The temperature is decreased and the volume is measured again.

1. Graph this table on the coordinate plane provided below.

2. Find the equation of the line that passes through the points you graphed in Exercise 1.

v � t � 182

3. Use the equation you found in Exercise 2 to find the temperature that would give a volume of zero. This temperature is the lowest one possible and is called absolute zero.

�273�C

4. In 1848, Lord Kelvin proposed a new temperature scale with 0 being assigned to absolute zero. The size of the degree chosen was the same size as the Celsius degree. Change each of the Celsius temperatures in the table above to degrees Kelvin.

303�, 294�, 273�, 261�, 246�

2�3

t (�C)

V(mL)

O

200

100

10�10�20�30 20 30

Temperature (t ) Volume (V )

30°C 202 mL21°C 196 mL0°C 182 mL

–12°C 174 mL–27°C 164 mL

Enrichment

NAME ______________________________________________ DATE______________ PERIOD _____

5-45-4

Study Guide and InterventionWriting Equations in Point-Slope Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-55-5


Less

on

5-5

Point-Slope Form

Point-Slope Formy � y1 � m(x � x1), where (x1, y1) is a given point on a nonvertical line and m is the slope of the line

Write the point-slope formof an equation for a line that passes through (6, 1) and has a slope of � .

y � y1 � m(x � x1) Point-slope form

y � 1 � � (x � 6) m � � ; (x1, y1) � (6, 1)

Therefore, the equation is y � 1� � (x � 6).5�2

5�2

5�2

5�2

Write the point-slopeform of an equation for a horizontalline that passes through (4, �1).

y � y1 � m(x � x1) Point-slope form

y � (�1) � 0(x � 4) m � 0; (x1, y1) � (4, �1)

y � 1 � 0 Simplify.

Therefore, the equation is y � 1 � 0.


ExercisesExercises

Write the point-slope form of an equation for a line that passes through eachpoint with the given slope.

1. 2. 3.

4. (2, 1), m � 4 5. (�7, 2), m � 6 6. (8, 3), m � 1

7. (�6, 7), m � 0 8. (4, 9), m � 9. (�4, �5), m � �

10. Write the point-slope form of an equation for the horizontal line that passes through (4, �2).

11. Write the point-slope form of an equation for the horizontal line that passes through (�5, 6).

12. Write the point-slope form of an equation for the horizontal line that passes through (5, 0).

1�2

3�4

(2, –3)

x

y

O

m � –2

(–3, 2)

x

y

O

m � 0(4, 1)

x

y

O

m � 1


Forms of Linear Equations


y � mx � b m � slope; b � y-intercept

Point-Slope Form

y � y1 � m(x � x1) m � slope; (x1, y1) is a given point.

Standard Ax � By � C A and B are not both zero. Usually A is nonnegative and A, B, and CForm are integers whose greatest common factor is 1.


Writing Equations in Point-Slope Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-55-5

Write y � 5 � (x � 6) instandard form.

y � 5 � (x � 6) Original equation

3( y � 5) � 3� �(x � 6) Multiply each side by 3.

3y � 15 � 2(x � 6) Distributive Property

3y � 15 � 2x � 12 Distributive Property

3y � 2x � 27 Subtract 15 from each side.

�2x � 3y � �27 Add �2x to each side.

2x � 3y � 27 Multiply each side by �1.

Therefore, the standard form of the equationis 2x � 3y � 27.

2�3

2�3

2�3

Write y � 2 � � (x � 8)in slope-intercept form.

y � 2 � � (x � 8) Original equation

y � 2 � � x � 2 Distributive Property

y � � x � 4 Add 2 to each side.

Therefore, the slope-intercept form of the

equation is y � � x � 4.1�4

1�4

1�4

1�4

1�4


Write each equation in standard form.

1. y � 2 � �3(x � 1) 2. y � 1 � � (x � 6) 3. y � 2 � (x � 9)

4. y � 3 � �(x � 5) 5. y � 4 � (x � 3) 6. y � 4 � � (x � 1)

Write each equation in slope-intercept form.

7. y � 4 � 4(x � 2) 8. y � 5 � (x � 6) 9. y � 8 � � (x � 8)

10. y � 6 � 3�x � � 11. y � 4 � �2(x � 5) 12. y � � (x � 2)1�2

5�3

1�3

1�4

1�3

2�5

5�3

2�3

1�3

ExercisesExercises

Skills PracticeWriting Equations in Point-Slope Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-55-5


Less

on

5-5


1. 2. 3.

4. (3, 1), m � 0 5. (�4, 6), m � 8 6. (1, �3), m � �4

7. (4, �6), m � 1 8. (3, 3), m � 9. (�5, �1), m � �


10. y � 1 � x � 2 11. y � 9 � �3(x � 2) 12. y � 7 � 4(x � 4)

13. y � 4 � �(x � 1) 14. y � 6 � 4(x � 3) 15. y � 5 � �5(x � 3)

16. y � 10 � �2(x � 3) 17. y � 2 � � (x � 4) 18. y � 11 � (x � 3)


19. y � 4 � 3(x � 2) 20. y � 2 � �(x � 4) 21. y � 6 � �2(x � 2)

22. y � 1 � �5(x � 3) 23. y � 3 � 6(x � 1) 24. y � 8 � 3(x � 5)

25. y � 2 � (x � 6) 26. y � 1 � � (x � 9) 27. y � � x �1�2

1�2

1�3

1�2

1�3

1�2

5�4

4�3

(2, –3)

x

y

O

m � 0

(1, –2)x

y

O

m � –1

(–1, –2)x

y

O

m � 3



1. (2, 2), m � �3 2. (1, �6), m � �1 3. (�3, �4), m � 0

4. (1, 3), m � � 5. (�8, 5), m � � 6. (3, �3), m �


7. y � 11 � 3(x � 2) 8. y � 10 � �(x � 2) 9. y � 7 � 2(x � 5)

10. y � 5 � (x � 4) 11. y � 2 � � (x � 1) 12. y � 6 � (x � 3)

13. y � 4 � 1.5(x � 2) 14. y � 3 � �2.4(x � 5) 15. y � 4 � 2.5(x � 3)


16. y � 2 � 4(x � 2) 17. y � 1 � �7(x � 1) 18. y � 3 � �5(x � 12)

19. y � 5 � (x � 4) 20. y � � �3�x � � 21. y � � �2�x � �

CONSTRUCTION For Exercises 22–24, use the following information.A construction company charges $15 per hour for debris removal, plus a one-time fee for theuse of a trash dumpster. The total fee for 9 hours of service is $195.

22. Write the point-slope form of an equation to find the total fee y for any number of hours x.

23. Write the equation in slope-intercept form.

24. What is the fee for the use of a trash dumpster?

MOVING For Exercises 25–27, use the following information.There is a set daily fee for renting a moving truck, plus a charge of $0.50 per mile driven.It costs $64 to rent the truck on a day when it is driven 48 miles.

25. Write the point-slope form of an equation to find the total charge y for any number ofmiles x for a one-day rental.

26. Write the equation in slope-intercept form.

27. What is the daily fee?

1�4

2�3

1�4

1�4

3�2

4�3

3�4

3�2

1�3

2�5

3�4

Practice Writing Equations in Point-Slope Form

NAME ______________________________________________ DATE ____________ PERIOD _____

5-55-5

Reading to Learn MathematicsWriting Equations in Point-Slope Form

NAME ______________________________________________ DATE______________ PERIOD _____

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on

5-5

Pre-Activity How can you use the slope formula to write an equation of a line?


Note that in the final equation there is a value subtracted from x and from y. What are these values?The value subtracted from x is the x-coordinate of the givenpoint. The value subtracted from y is the y-coordinate of thegiven point.

Reading the Lesson

1. In the formula y � y1 � m(x � x1), what do x1 and y1 represent?

x1 and y1 represent the coordinates of any given point on the graph of the line.

2. Complete the chart below by listing three forms of equations. Then write the formula foreach form. Finally, write three examples of equations in those forms.Sample examples are given.

Form of Equation Formula Example

slope-intercept y � mx � b y � 3x � 2

point-slope y � y1 � m(x � x1) y � 2 � 4(x � 3)

standard Ax � By � C 3x � 5y � 15

3. Refer to Example 5 on page 288 of your textbook. What do you think the hypotenuse of aright triangle is? Sample answers: The hypotenuse is the longest side ofthe right triangle. The hypotenuse is the side opposite the right angle ina right triangle.


4. Suppose you could not remember all three formulas listed in the table above. Which ofthe forms would you concentrate on for writing linear equations? Explain why you chosethat form. Sample answer: Point-slope form; the slope-intercept form can be written from the point-slope form. This is so because the y-intercept lets you write the coordinates of the point where the linecrosses the y-axis. You can use that point as the given point in the point-slope formula.


Collinearity You have learned how to find the slope between two points on a line. Doesit matter which two points you use? How does your choice of points affectthe slope-intercept form of the equation of the line?

1. Choose three different pairs of points from the graph at the right. Write the slope-intercept form of the line using each pair.

2. How are the equations related?

3. What conclusion can you draw from your answers to Exercises 1 and 2?

When points are contained in the same line, they are said to be collinear.Even though points may look like they form a straight line when connected,it does not mean that they actually do. By checking pairs of points on a line you can determine whether the line represents a linear relationship.

4. Choose several pairs of points from the graph at the right and write the slope-intercept form of the line using each pair.

5. What conclusion can you draw from your equations in Exercise 4? Is this a straight line?

x

y

O

x

y

O

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

5-55-5

Study Guide and InterventionGeometry: Parallel and Perpendicular Lines

NAME ______________________________________________ DATE ____________ PERIOD _____

5-65-6


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on

5-6

Parallel Lines Two nonvertical lines are parallel if they have the same slope. All vertical lines are parallel.

Write the slope-intercept form for an equation of the line thatpasses through (�1, 6) and is parallel to the graph of y � 2x � 12.

A line parallel to y � 2x � 12 has the same slope, 2. Replace m with 2 and (x1, y1) with (�1, 6) in the point-slope form.y � y1 � m(x � x1) Point-slope form

y � 6 � 2(x � (�1)) m � 2; (x1, y1) � (�1, 6)

y � 6 � 2(x � 1) Simplify.

y � 6 � 2x � 2 Distributive Property

y � 2x � 8 Slope-intercept form

Therefore, the equation is y � 2x � 8.

Write the slope-intercept form for an equation of the line that passes through thegiven point and is parallel to the graph of each equation.

1. 2. 3.

4. (�2, 2), y � 4x � 2 5. (6, 4), y � x � 1 6. (4, �2), y � �2x � 3

7. (�2, 4), y � �3x � 10 8. (�1, 6), 3x � y � 12 9. (4, �6), x � 2y � 5

10. Find an equation of the line that has a y-intercept of 2 that is parallel to the graph ofthe line 4x � 2y � 8.

11. Find an equation of the line that has a y-intercept of �1 that is parallel to the graph ofthe line x � 3y � 6.

12. Find an equation of the line that has a y-intercept of �4 that is parallel to the graph ofthe line y � 6.

1�3

(–3, 3)

x

y

O

4x � 3y � –12

(–8, 7)

x

y

O

y � – 12x � 4

2

2

(5, 1)x

y

O

y � x � 8

ExampleExample

ExercisesExercises


Perpendicular Lines Two lines are perpendicular if their slopes are negativereciprocals of each other. Vertical and horizontal lines are perpendicular.

Write the slope-intercept form for an equation that passes through(�4, 2) and is perpendicular to the graph of 2x � 3y � 9.

Find the slope of 2x � 3y � 9.2x � 3y � 9 Original equation

�3y � �2x � 9 Subtract 2x from each side.

y � x � 3 Divide each side by �3.

The slope of y � x � 3 is . So, the slope of the line passing through (�4, 2) that is 2�3

2�3

2�3


Geometry: Parallel and Perpendicular Lines

NAME ______________________________________________ DATE ____________ PERIOD _____

5-65-6

ExampleExample

ExercisesExercises

perpendicular to this line is the negative reciprocal of , or � .Use the point-slope form to find the equation.y � y1 � m(x � x1) Point-slope form

y � 2 � � (x � (�4)) m � � ; (x1, y1) � (�4, 2)

y � 2 � � (x � 4) Simplify.

y � 2 � � x � 6 Distributive Property

y � � x � 4 Slope-intercept form

Write the slope-intercept form for an equation of the line that passes through thegiven point and is perpendicular to the graph of each equation.

1. (4, 2), y � x � 1 2. (2, �3), y � � x � 4 3. (6, 4), y � 7x � 1

4. (�8, �7), y � �x � 8 5. (6, �2), y � �3x � 6 6. (�5, �1), y � x � 3

7. (�9, �5), y � �3x � 1 8. (�1, 3), 2x � 4y � 12 9. (6, �6), 3x � y � 6

10. Find an equation of the line that has a y-intercept of �2 and is perpendicular to thegraph of the line x � 2y � 5.

11. Find an equation of the line that has a y-intercept of 5 and is perpendicular to the graphof the line 4x � 3y � 8.

5�2

2�3

1�2

3�2

3�2

3�2

3�2

3�2

3�2

2�3

Skills PracticeGeometry: Parallel and Perpendicular Lines

NAME ______________________________________________ DATE ____________ PERIOD _____

5-65-6


Less

on

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Write the slope-intercept form of an equation of the line that passes through thegiven point and is parallel to the graph of each equation.

1. 2. 3.

4. (3, 2), y � 3x � 4 5. (�1, �2), y � �3x � 5 6. (�1, 1), y � x � 4

7. (1, �3), y � �4x � 1 8. (�4, 2), y � x � 3 9. (�4, 3), y � x � 6

10. (4, 1), y � � x � 7 11. (�5, �1), 2y � 2x � 4 12. (3, �1), 3y � x � 9

Write the slope-intercept form of an equation of the line that passes through thegiven point and is perpendicular to the graph of each equation.

13. (�3, �2), y � x � 2 14. (4, �1), y � 2x � 4 15. (�1, �6), x � 3y � 6

16. (�4, 5), y � �4x � 1 17. (�2, 3), y � x � 4 18. (0, 0), y � x � 1

19. (3, �3), y � x � 5 20. (�5, 1), y � � x � 7 21. (0, �2), y � �7x � 3

22. (2, 3), 2x � 10y � 3 23. (�2, 2), 6x � 3y � �9 24. (�4, �3), 8x � 2y � 16

5�3

3�4

1�2

1�4

1�4

1�2

(–2, 2)

x

y

O

y � 12x � 1(1, –1)

x

y

O

y � –x � 3

(–2, –3)

x

y

O

y � 2x � 1


Write the slope-intercept form of an equation of the line that passes through thegiven point and is parallel to the graph of each equation.

1. (3, 2), y � x � 5 2. (�2, 5), y � �4x � 2 3. (4, �6), y � � x � 1

4. (5, 4), y � x � 2 5. (12, 3), y � x � 5 6. (3, 1), 2x � y � 5

7. (�3, 4), 3y � 2x � 3 8. (�1, �2), 3x � y � 5 9. (�8, 2), 5x � 4y � 1

10. (�1, �4), 9x � 3y � 8 11. (�5, 6), 4x � 3y � 1 12. (3, 1), 2x � 5y � 7

Write the slope-intercept form of an equation of the line that passes through thegiven point and is perpendicular to the graph of each equation.

13. (�2, �2), y � � x � 9 14. (�6, 5), x � y � 5 15. (�4, �3), 4x � y � 7

16. (0, 1), x � 5y � 15 17. (2, 4), x � 6y � 2 18. (�1, �7), 3x � 12y � �6

19. (�4, 1), 4x � 7y � 6 20. (10, 5), 5x � 4y � 8 21. (4, �5), 2x � 5y � �10

22. (1, 1), 3x � 2y � �7 23. (�6, �5), 4x � 3y � �6 24. (�3, 5), 5x � 6y � 9

25. GEOMETRY Quadrilateral ABCD has diagonals A�C� and B�D�.Determine whether A�C� is perpendicular to B�D�. Explain.

26. GEOMETRY Triangle ABC has vertices A(0, 4), B(1, 2), and C(4, 6).Determine whether triangle ABC is a right triangle. Explain.

x

y

O

A

D

C

B

1�3

4�3

2�5

3�4

Practice Geometry: Parallel and Perpendicular Lines

NAME ______________________________________________ DATE ____________ PERIOD _____

5-65-6

Reading to Learn MathematicsGeometry: Parallel and Perpendicular Lines

NAME ______________________________________________ DATE______________ PERIOD _____

5-65-6


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5-6

Pre-Activity How can you determine whether two lines are parallel?


• What is a family of graphs? A group of graphs that have at leastone characteristic in common, such as slope or y-intercept.

• Do you think lines that do not appear to intersect are parallel orperpendicular? parallel

Reading the Lesson

1. Refer to the Key Concept box on page 292. Why does the definition use the termnonvertical when talking about lines with the same slope? Vertical lines haveslopes that are undefined so we cannot say they have the same slope.

2. What is a right angle? Sample answers: A right angle is one that measures90°. It is an angle formed by perpendicular lines.

3. Refer to the Key Concept box on page 293. Describe how you find the opposite reciprocalof a number. Sample answer: The reciprocal of a given number is thenumber formed when you switch the numerator and denominator. Thenyou give it the opposite sign of the original number.

4. Write the opposite reciprocal of each number.

a. 2 � b. �3 c. � d. � 5


5. One way to remember how slopes of parallel lines are related is to say “same direction,same slope.” Try to think of a phrase to help you remember that perpendicular lineshave slopes that are opposite reciprocals.

Sample answer: Nicely right angles formed, use opposite reciprocals.

1�5

13�12

12�13

1�3

1�2


Pencils of LinesAll of the lines that pass through a single point in the same plane are called a pencil of lines.

All lines with the same slope,but different intercepts, are also called a “pencil,” a pencil of parallel lines.

Graph some of the lines in each pencil.

1. A pencil of lines through the 2. A pencil of lines described by point (1, 3) y � 4 � m(x � 2), where m is any

real number

3. A pencil of lines parallel to the line 4. A pencil of lines described by x � 2y � 7 y � mx � 3m � 2

x

y

Ox

y

O

x

y

Ox

y

O

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

5-65-6

Study Guide and InterventionScatter Plots and Lines of Fit

NAME ______________________________________________ DATE ____________ PERIOD _____

5-75-7


Less

on

5-7

Interpret Points on a Scatter Plot A scatter plot is a graph in which two sets ofdata are plotted as ordered pairs in a coordinate plane. If y increases as x increases, there isa positive correlation between x and y. If y decreases as x increases, there is a negativecorrelation between x and y. If x and y are not related, there is no correlation.

EARNINGS The graph at the right shows the amount of money Carmen earned eachweek and the amount she deposited in her savingsaccount that same week. Determine whether thegraph shows a positive correlation, a negativecorrelation, or no correlation. If there is a positive or negative correlation, describe itsmeaning in the situation.

The graph shows a positive correlation. The more Carmen earns, the more she saves.

Determine whether each graph shows a positive correlation, a negativecorrelation, or no correlation. If there is a positive correlation, describe it.

1. 2.

3. 4.Number of Mutual Funds

Years Since 1991

Nu

mb

er o

f Fu

nd

s(t

ho

usa

nd

s)

0 2 41 3 5 6 7

7

6

5

4

3

Source: The Wall Street Journal Almanac

Growth of Investment Clubs

Years Since 1990

Nu

mb

er o

f C

lub

s(t

ho

usa

nd

s)

0 2 41 3 5 6 7 8

35

28

21

14

7

Source: The Wall Street Journal Almanac

Average Jogging Speed

Minutes

Mile

s p

er H

ou

r

0 10 205 15 25

10

5

Average Weekly Work Hours in U.S.

Years Since 1990

Ho

urs

0 2 4 61 7 8 9 x

y

3 5

34.8

34.6

34.4

34.2


Carmen’s Earnings and Savings

Dollars Earned

Do

llars

Sav

ed

0 40 80 120

35

30

25

20

15

10

5

ExampleExample

ExercisesExercises


Lines of Fit

The table below shows the number of students per computer inUnited States public schools for certain school years from 1990 to 2000.

Year 1990 1992 1994 1996 1998 2000

Students per Computer 22 18 14 10 6.1 5.4

a. Draw a scatter plot and determine what relationship exists, if any.Since y decreases as x increases, the correlation is negative.

b. Draw a line of fit for the scatter plot.Draw a line that passes close to most of thepoints. A line of fit is shown.

c. Write the slope-intercept form of anequation for the line of fit.The line of fit shown passes through (1993, 16) and (1999, 5.7). Find the slope.

m �

m � �1.7

Find b in y � �1.7x � b.16 � �1.7 1993 � b

3404 � b Therefore, an equation of a line of fit is y � �1.7x � 3404.

Refer to the table for Exercises 1–3.

1. Draw a scatter plot. 3. Write the slope-intercept

2. Draw a line of fit for the data. form of an equation for theline of fit.

U.S. ProductionWorkers Hourly Wage

Years Since 1995

Ho

url

y W

age

(do

llars

)

0 1 32 4 5 6 7

14

13

12

11


Years Hourly Since 1995 Wage

0 $11.43

1 $11.82

2 $12.28

3 $12.78

4 $13.24

5.7 � 16��1999 � 1993

Students per Computerin U.S. Public Schools

Year

Stu

den

ts p

er C

om

pu

ter

1990 1992 1994 1996 1998 2000

24

20

16

12

8

4

0



Scatter Plots and Lines of Fit

NAME ______________________________________________ DATE ____________ PERIOD _____

5-75-7

ExampleExample

ExercisesExercises

Skills PracticeStatistics: Scatter Plots and Lines of Fit

NAME ______________________________________________ DATE ____________ PERIOD _____

5-75-7


Less

on

5-7

Determine whether each graph shows a positive correlation, a negativecorrelation, or no correlation. If there is a positive or negative correlation,describe its meaning in the situation.

1. 2.

3. 4.

BASEBALL For Exercises 5–7, use the scatterplot that shows the average price of a major-league baseball ticket from 1991 to 2000.

5. Determine what relationship, if any, exists in the data. Explain.

6. Use the points (1993, 9.60) and (1998, 13.60) to write the slope-intercept form of an equationfor the line of fit shown in the scatter plot.

7. Predict the price of a ticket in 2004.

Baseball Ticket Prices

Year

Ave

rag

e Pr

ice

($)

’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99

18

16

14

12

10

8

0’00

Source: Team Marketing Report, Chicago

Evening Newspapers

Year

Nu

mb

er o

f N

ewsp

aper

s

’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99

1050

1000

950

900

850

800

750

0

Source: Editor & Publisher

Weight-Lifting

Weight (pounds)

Rep

etit

ion

s

0 40 8020 60 100120140

14

12

10

8

6

4

2

Library Fines

Books Borrowed

Fin

es (

do

llars

)

0 2 4 5 6 7 8 81 3 10

7

6

5

4

3

2

1

Calories BurnedDuring Exercise

Time (minutes)

Cal

ori

es

0 20 4010 30 50 60

600

500

400

300

200

100


Determine whether each graph shows a positive correlation, a negativecorrelation, or no correlation. If there is a positive or negative correlation,describe its meaning in the situation.

1. 2.

DISEASE For Exercises 3–6, use the table that shows the number of cases of mumps in the United States for the years 1995 to 1999.

3. Draw a scatter plot and determine what relationship, if any, exists in the data.

Source: Centers for Disease Control and Prevention

4. Draw a line of fit for the scatter plot.

5. Write the slope-intercept form of an equation for theline of fit.

6. Predict the number of cases in 2004.

ZOOS For Exercises 7–10, use the table that shows the average and maximum longevity ofvarious animals in captivity.

7. Draw a scatter plot and determine what relationship, if any, exists in the data. Source: Walker’s Mammals of the World

8. Draw a line of fit for the scatter plot.

9. Write the slope-intercept form of an equation for the line of fit.

10. Predict the maximum longevity for an animal with an average longevity of 33 years.

Longevity (years)

Avg. 12 25 15 8 35 40 41 20

Max. 47 50 40 20 70 77 61 54

U.S. Mumps Cases

Year

Cas

es

1995 1997 1999 2001

1000

800

600

400

200

0

U.S. Mumps Cases

Year 1995 1996 1997 1998 1999

Cases 906 751 683 666 387

State Elevations

Mean Elevation (feet)

Hig

hes

t Po

int

(th

ou

san

ds

of

feet

)

10000 2000 3000

16

12

8

4

Source: U.S. Geological Survey

Temperature versus Rainfall

Average Annual Rainfall (inches)

Ave

rag

eTe

mp

erat

ure

(�F

)

10 15 20 25 30 35 40 45

64

60

56

52

0

Source: National Oceanic and Atmospheric Administration

Practice Statistics: Scatter Plots and Lines of Fit

NAME ______________________________________________ DATE ____________ PERIOD _____

5-75-7

Reading to Learn MathematicsStatistics: Scatter Plots and Lines of Fit

NAME ______________________________________________ DATE______________ PERIOD _____

5-75-7


Less

on

5-7

Pre-Activity How do scatter plots help identify trends in data?


• What does the phrase linear relationship mean to you? Sampleanswer: It means that when you graph the data points on acoordinate grid, the points all lie on or close to a line thatyou could draw on the grid.

• Write three ordered pairs that fit the description as x increases, ydecreases. Sample answer: {(2, 5), (3, 3), (4, 1)}

Reading the Lesson

1. Look up the word scatter in a dictionary. How does this definition compare to the termscatter plot? One definition states “to occur or fall irregularly or atrandom.”The points in a scatter plots usually do not follow an exactlinear pattern, but fall irregularly on the coordinate plane.

2. What is a line of fit? How many data points fall on the line of fit? A line of fit showsthe trend of the data. It is impossible to say how many data points mayfall on a line of fit—maybe several, maybe none.

3. What is linear interpolation? How can you distinguish it from linear extrapolation?Linear interpolation is the process of predicting a y-value for a given x-value that lies between the least and greatest x-values in the data set.“Inter-” means between and “extra-” means beyond. If the x-value isbetween the extremes of the x-values in the data set, you sayinterpolation; if the x-value is less than or greater than the extremes,you say extrapolation.


4. How can you remember whether a set of data points shows a positive correlation or anegative correlation? If it looks like a line of fit for the points would have apositive slope, there is a positive correlation. If it looks like a line of fitwould have a negative slope, there is a negative correlation.


Latitude and Temperature The latitude of a place on Earthis the measure of its distancefrom the equator. What do youthink is the relationship between a city’s latitude and its January temperature? At the right is a table containing the latitudes and January mean temperatures for fifteenU.S. cities.

Sources: www.indo.com and www.nws.noaa.gov/climatex.html

1. Use the information in the table to create a scatter plot and draw a line of best fit for the data.

2. Write an equation for the line of fit. Make a conjecture about the relationship between a city’s latitude and its meanJanuary temperature.

3. Use your equation to predict the Januarymean temperature of Juneau, Alaska,which has latitude 58:23 N.

4. What would you expect to be the latitude of a city with a January mean temperature of 15°F?

5. Was your conjecture about the relationship between latitude and temperature correct?

6. Research the latitudes and temperatures for cities in the southern hemisphere instead.Does your conjecture hold for these cities as well?

Latitude (�N)

Tem

per

atu

re (

�F)

70

60

50

40

30

20

10

0

�10

T

L20 40 6010 30 50

U.S. City Latitude January Mean Temperature

Albany, New York 42:40 N 20.7°F

Albuquerque, New Mexico 35:07 N 34.3°F

Anchorage, Alaska 61:11 N 14.9°F

Birmingham, Alabama 33:32 N 41.7°F

Charleston, South Carolina 32:47 N 47.1°F

Chicago, Illinois 41:50 N 21.0°F

Columbus, Ohio 39:59 N 26.3°F

Duluth, Minnesota 46:47 N 7.0°F

Fairbanks, Alaska 64:50 N �10.1°F

Galveston, Texas 29:14 N 52.9°F

Honolulu, Hawaii 21:19 N 72.9°F

Las Vegas, Nevada 36:12 N 45.1°F

Miami, Florida 25:47 N 67.3°F

Richmond, Virginia 37:32 N 35.8°F

Tucson, Arizona 32:12 N 51.3°F

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

5-75-7

Chapter 5 Test, Form 1

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Write the letter for the correct answer in the blank at the right of each question.For Questions 1–4, find the slope of each line described.

1. the line through (3, 7) and (�1, 4)

A. �43� B. �

34� C. �

121� D. �1

21�

1.

2. the line through (�3, 2) and (6, 2)

A. �49� B. �

43� C. 0 D. undefined 2.

3. the line graphed at the right

A. �23� B. �

32�

C. ��32� D. ��

23� 3.

4. a vertical lineA. 1 B. 0 C. �1 D. undefined 4.

5. Which graph has a slope of �3?A. B. C. D. 5.

6. COMMUNICATION In 1996, there were 171 area codes in the United States.In 1999, there were 285. Find the rate of change from 1996 to 1999.

A. 114 B. 38 C. �318�

D. �144 6.

For Questions 7–9, find the equation in slope-intercept form that describes each line.

7. a line through (2, 4) with slope 0A. y � 2 B. x � 2 C. y � 4 D. x � 4 7.

8. a line through (4, 2) with slope �12�

A. y � ��12�x B. y � �

12�x � 4 C. y � 2x � 10 D. y � �

12�x 8.

9. a line through (�1, 1) and (2, 3)

A. y � �23�x � �

53� B. y � ��

23�x � �

53� C. y � �

23�x � �

53� D. y � ��

23�x � �

53� 9.

10. If 5 deli sandwiches cost $29.75, how much will 8 sandwiches cost?A. $37.75 B. $29.75 C. $47.60 D. $0.16 10.

11. What is the standard form of y � 8 � 2(x � 3)?A. 2x � y � 14 B. y � 2x � 14 C. 2x � y � �14 D. y � 2x � 11 11.

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Chapter 5 Test, Form 1 (continued)

12. Which is the graph of y � ��34�x?

A. B. C. D. 12.

13. Which is the point-slope form of an equation for the line that passes through (0, �5) with slope 2?A. y � 2x � 5 B. y � 5 � 2x C. y � 5 � x � 2 D. y � 2(x � 5) 13.

14. What is the slope-intercept form of y � 6 � 2(x � 2)?A. y � 2x � 6 B. y � 2x � 2 C. y � 2x � 6 D. 2x � y � 6 14.

15. When are two lines parallel?A. when the slopes are opposite B. when the slopes are equalC. when the product of the slopes is 1 D. when the slopes are positive 15.

16. Find the slope-intercept form of an equation for the line that passes through (�1, 2) and is parallel to y � 2x � 3.A. y � 2x � 4 B. y � 0.5x � 4 C. y � 2x � 3 D. y � �0.5x � 4 16.

17. Find the slope-intercept form of an equation of the line perpendicular to the graph of x � 3y � 5 and passing through (0, 6).

A. y � �13�x � 2 B. y � �3x � 6 C. y � �

13�x � 2 D. y � 3x � 6 17.

For Questions 18 and 19, use the scatter plot at the right.

18. How would you describe the relationship between the x and y values in the scatter plot?A. strong negative correlationB. weak negative correlationC. weak positive correlationD. strong positive correlation 18.

19. Based on the data in the scatter plot, what would you expect the y value to be for x � 2010?A. greater than 80 B. between 80 and 65C. between 65 and 50 D. less than 50 19.

20. What is an equation of the line whose graph has slope of 2 and a y-intercept of �5?A. y � �5x � 2 B. y � 5x � 2 C. y � 2x � 5 D. y � 2x � 5 20.

Bonus Find the value of r in (4, r), (r, 2) so that the slope of the

line containing them is ��53�. B:

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'80 '85 '90 '95 '00

Chapter 5 Test, Form 2A

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Ass

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Write the letter for the correct answer in the blank at the right of each question.

1. What is the slope of the line through (1, 9) and (�3, 16)?

A. ��74� B. ��

47� C. ��

225� D. ��2

25�

1.

2. What is the slope of the line through (�4, 3) and (5, 3)? A. 0 B. undefined C. 9 D. 1 2.

3. Find the value of r so that the line through (8, r) and (4, 5) has a slope of �4.A. 11 B. �11 C. 4 D. �4 3.

4. In 1995, there were 12,000 students at Beacon High. In 2000, there were 12,250. What is the rate of change in the number of students?A. 250/yr B. 50/yr C. 42/yr D. 200/yr 4.

5. Which is the graph of y � �23�x?

A. B. C. D. 5.

6. If y varies directly as x and y � 3 when x � 10, find x when y � 8.

A. �830� B. �

152� C. �

145� D. none of these 6.

7. A driver’s distance varies directly as the amount of time traveled. After 6 hours, a driver had traveled 390 miles. How far had the driver traveled after 4 hours?A. 130 miles B. 220 miles C. 260 miles D. 650 miles 7.

8. A line of fit might be defined asA. a line that connects all the data points.B. a line that might best estimate the data and be used for predicting values.C. a vertical line halfway through the data.D. a line whose slope is greater than 1. 8.

9. What is the slope-intercept form of the equation of a line with slope 5 and y-intercept �8?A. y � �8x � 5 B. y � 8x � 5 C. 5x � y � � 8 D. y � 5x � 8 9.

10. Which equation is graphed at the right?A. 2y � x �10 B. 2x � y � �5C. 2x � y � 5 D. 2y � x � �5 10.

11. Which is an equation of the line that passes through (2, �5) and (6, 3)?

A. y � �12�x � 6 B. y � �

12�x

C. y � 2x � 12 D. y � 2x � 9 11.

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Chapter 5 Test, Form 2A (continued)

12. What is the standard form of the equation of the line through (0, �3) with

slope �25�?

A. �5x � 2y � 15 B. �5x � 2y � �15C. 2x � 5y � 15 D. �2x � 5y � 15 12.

13. Which is an equation of the line with slope �3 and a y-intercept of 5?A. y � �3(x � 5) B. y � 5 � �3x C. �3x � y � 5 D. y � 5x � 3 13.

14. What is the standard form of y � 7 � ��23�(x �1)?

A. �2x � 3y � 23 B. �3x � 2y � 17 C. 2x � 3y � 19 D. 3x � 2y � 11 14.

15. What is the equation of the line through (�2, �3) with a slope of 0?A. x � �2 B. y � �3 C. �2x � 3y � 0 D. �3x � 2y � 0 15.

16. Find the slope-intercept form of the equation of the line that passes through (�5, 3) and is parallel to 12x � 3y � 10.A. y � �4x � 17 B. y � 4x � 13 C. y � � 4x � 13 D. y � 4x � 23 16.

17. If line q has a slope of ��38�, what is the slope of any line perpendicular to q?

A. ��38� B. �

38� C. �

83� D. ��

83� 17.


18. Which data are shown by the scatter plot?A. (1980, 5.5), (1982, 6.1), (1989, 7.6)B. (1980, 5.5), (1985, 6.1), (1989, 7.6)C. (1980, 5.5), (1985, 6.6), (1990, 8.0)D. (1980, 5.5), (1982, 6.6), (1990, 8.0) 18.

19. Based on the data in the scatter plot, what would you expect the y value to be for x � 1995?A. between 7 and 8 B. higher than 8C. between 5 and 7 D. impossible to tell 19.

20. To calculate the charge for a load of bricks, including delivery, the Redstone Brick Co. uses the equation C � 0.42b � 25, where C is the charge and b is the number of bricks. What is the delivery fee per load?A. $42 B. $67C. $25 D. It depends on the number of bricks 20.

Bonus What is the y-intercept of a line through (2, 7) and

perpendicular to the line y � ��32�x � 6? B:

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'80 '85 '90

Chapter 5 Test, Form 2B

NAME DATE PERIOD

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Write the letter for the correct answer in the blank at the right of each question.1. What is the slope of the line through (2, �8) and (4, 1)?

A. ��29� B. ��

67� C. ��

76� D. �

92� 1.

2. What is the slope of the line through (�4, �6) and (9, �6)?

A. ��152� B. ��1

52�

C. 0 D. undefined 2.

3. Find the value of r so that the line through (8, 5) and (4, r) has a slope of �4.A. 21 B. �21 C. 11 D. �11 3.

4. In 1995, MusicMart sold 12,000 CDs. In 2000, they sold 14,550 CDs. What is the rate of change in the number of CDs sold?A. 2550/yr B. 510/yr C. 425/yr D. 2400/yr 4.

5. Which is the graph of y � ��12�x?

A. B. C. D. 5.

6. If y varies directly as x and y � 5 when x � 8, find y when x � 9.

A. �752� B. �

485� C. �

490� D. 6 6.

7. The amount a spring stretches varies directly as the weight of the object attached to it. If an 8-ounce weight stretches a spring 10 centimeters, how much weight will stretch it 15 centimeters?A. 16 oz B. 6 oz C. 10 oz D. 12 oz 7.

8. The graph of data that has a strong negative correlation has A. a narrow linear pattern from lower left to upper right.B. a narrow linear pattern from upper left to lower right.C. a narrow horizontal pattern below the x-axis.D. all negative x-values. 8.

9. What is the slope-intercept form of the equation of the line with slope �14�

and y-intercept at the origin?

A. y � 4x B. y � �14�x C. y � x � �

14� D. y � �

14� � x 9.

10. Which equation is graphed at the right?A. y � 2x � �4 B. 2x � y � �4C. 2x � y � 4 D. y �4 � 2x 10.

11. Which is an equation of the line that passes through (4, �5) and (6, �9)?

A. y � �12�x � 3 B. y � �

12�x � 3 C. y � �2x � 3 D. y � 2x � 3 11.

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Chapter 5 Test, Form 2B (continued)

12. What is the standard form of the equation of the line through (6, �3) with

slope �23�?

A. �2x � 3y � 24 B. 2x � 3y � 21 C. 3x � 2y � 24 D. 3x � 2y � �21 12.

13. Which is an equation of the line with slope �3 that passes through (2, 4)?A. y � 4 � �3(x � 2) B. y � 4 � �3x � 2C. y � 4 � �3(x � 2) D. y �2 � �3(x � 4) 13.

14. What is the standard form of y � 2 � �12�(x � 4)?

A. x � 2y � 0 B. x � 2y � 8 C. 2x � y � 10 D. 4x � 2y � 0 14.

15. What is the equation of the line through (�2, �3) with an undefined slope?A. x � �2 B. y � �3 C. �2x � 3y � 0 D. �3x � 2y � 0 15.

16. Find the slope-intercept form of the equation of the line that passes through (�1, 5) and is parallel to 4x � 2y � 8.A. y � �2x � 9 B. y � 2x � 9 C. y � 4x � 9 D. y � �2x � 3 16.

17. If line q has a slope of �2, what is the slope of any line perpendicular to q?

A. 2 B. �2 C. �12� D. ��

12� 17.


18. Which data are shown by the scatter plot?A. (1970, 47), (1980, 31), (1986, 24)B. (1970, 50), (1985, 25), (1990, 0)C. (47, 1970), (31, 1980), (24, 1986)D. (1976, 45), (1980, 35), (1985, 8) 18.

19. Based on the data in the scatter plot,which statement is true?A. As x increases, y increases.B. As x increases, y decreases.C. There is no relationship between x and y.D. There are not enough data to determine the relationship between x and y. 19.

20. A baby blue whale weighed 3 tons at birth. Ten days later, it weighed 4 tons. Assuming the same rate of growth, which equation shows the weight w when the whale is d days old?A. w � 10d � 3 B. w � 10d � 4 C. w � 0.1d � 3 D. w � d � 10 20.

Bonus For what value of k does kx � 7y � 10 have a slope of 3? B:

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Chapter 5 Test, Form 2C


For Questions 1–3, find the slope of the line passing through each pair of points.If the slope is undefined, write “undefined.”

1. (2, 5) and (3, 6) 1.

2. (�1, 3) and (6, 3) 2.

3. (6, �4) and (�3, 7) 3.

4. Find the value of r so that the line through (�4, 8) and 4.

(r, �6) has a slope of �23�.

5. In 1968, vehicle emission standards allowed 5.6.3 hydrocarbons released per mile driven. By 1980, the standards allowed only 0.41 hydrocarbons per mile driven.What was the rate of change from 1968 to 1980?

6. Graph y � ��12�x. 6.

7. If a shark can swim 27 miles in 9 hours, how many miles 7.will it swim in 12 hours?

8. Write a linear equation in slope-intercept form to model the 8.situation: A telephone company charges $28.75 per month plus 10¢ a minute for long-distance calls.

9. Write an equation in standard form of the line that passes 9.through (7, �3) and has a y-intercept of 2.

10. Write the slope-intercept form of an 10.equation for the line graphed at the right.

11. Graph the line with y-intercept 3 and 11.

slope ��34�.

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Chapter 5 Test, Form 2C (continued)

12. Write an equation in slope-intercept form for the line that 12.passes through (�1, �2) and (3, 4).

13. Write an equation in standard form for the line whose slope 13.is undefined and passes through (�6, 4).

14. Write an equation in point-slope form for the line that has 14.

slope �13� and passes through (�2, 8).

15. Write the standard form of the equation y � 4 � ��172�(x � 1). 15.

16. Write the slope-intercept form of the equation 16.y � 2 � 3(x � 4).

17. Write the slope-intercept form of the equation of the line 17.parallel to the graph of 2x � y � 5 that passes through (0, 1).

18. Write the slope-intercept form of the equation of the line 18.

perpendicular to the graph of y � ��32�x � 7 that passes

through (3, �2).

For Questions 19 and 20, use the data in the table.

19. Make a scatter plot relating time spent studying to the 19.score received.

20. Write the slope-intercept form of the equation for a line 20.of fit for the data. Use your equation to predict a student’s score if the student spent 35 minutes studying.

Bonus In a certain lake, a 1-year-old bluegill fish is 3 inches B:long, while a 4-year-old bluegill fish is 6.6 inches long.Assuming the growth rate can be approximated by a linear equation, write an equation in slope-intercept form for the length � of a bluegill fish in inches after t years. Then use the equation to determine the age of a 9-inch bluegill.

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Time Spent Studying (min) 10 20 30 40 50

Score Received (percent) 53 67 78 87 95

Chapter 5 Test, Form 2D


For Questions 1–3, find the slope of the line passing through each pair of points.If the slope is undefined, write “undefined.”

1. (4, 1) and (�4, 1) 1.

2. (�2, 1) and (3, �2) 2.

3. (�6, 7) and (�6, �2) 3.

4. Find the value of r so that the line through (4, 5) and 4.

(r, 3) has a slope of �23�.

5. In 1983, 57.5% of college students graduated in 5 or fewer 5.years of study. In 1997, that number had fallen to 52.8%.What was the change of rate for percent of students graduating within 5 years from 1983 to 1997?

6. Graph y � �23�x. 6.

7. If a snail travels 200 inches in 2 hours, how long will it take 7.the snail to travel 50 inches?

8. Write a linear equation in slope-intercept form to model 8.the situation: An Internet company charges $4.95 per month plus $2.50 for each hour of use.

9. Write an equation in standard form of the line that passes 9.through (3, 1) and has a y-intercept of �2.

10. Write the slope-intercept form 10.of an equation for the line graphed at the right.

11. Graph the line with y-intercept 2 11.

and slope ��12�.

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Chapter 5 Test, Form 2D (continued)

12. Write an equation in slope-intercept form for the line that 12.passes through (5, 4) and (6, �1).

13. Write an equation in standard form for the line whose slope 13.is undefined that passes through (5, �3).

14. Write an equation in point-slope form for the line that has 14.

slope �43� and passes through (3, 0).

15. Write the standard form of the equation y � 3 � ��23�(x � 5). 15.

16. Write the slope-intercept form of the equation 16.

y � 1 � �34�(x � 3).

17. Write the slope-intercept form of the equation of the line 17.parallel to the graph of 9x � 3y � 6 that passes through (5, 3).

18. Write the slope-intercept form of the equation of the line 18.perpendicular to the graph of 4x � y � 12 that passes through (8, 2).

For Questions 19 and 20, use the data that shows age and percent of budget spent on entertainment in the table.

19. Make a scatter plot relating the age to the percent of the 19.person’s budget spent on entertainment.

20. Write the slope-intercept form of the equation for a line 20.of fit for the data. Use your equation to predict the percent of a 65-year-old person’s budget.

Bonus Write an equation in slope-intercept form of the line B:with y-intercept �6 and parallel to a line perpendicular to 5x � 6y � 13 � 0.

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Age 30 40 50 60 70 80

Percent Spent on Entertainment 6.1 6.0 5.4 5.0 4.7 3.4

Chapter 5 Test, Form 3


For Questions 1 and 2, find the slope of the line passing through each pair ofpoints. If the slope is undefined, write “undefined.”

1. (�8, 7) and (5, �2) 1.

2. (5, 9) and (5, �3) 2.

3. Find the value of r so that the line through (�4, 3) and (r, �3) 3.

has a slope of �23�.

4. Find the value of r so that the line through (r, 5) and (6, r) 4.

has a slope of �58�.

5. In 1990, there were approximately 35,000 people in 5.Lancaster. Five years later, the population was 38,452.Find the rate of change in the population.

6. Graph y � ��34�x. 6.

7. If an ostrich can run 15 kilometers in 15 minutes, how 7.many kilometers can it run in an hour?

8. Write the point-slope form of an equation of the line that has 8.

slope ��35� and passes through (2, 1).

9. Write an equation in standard form of the line that passes 9.through (2, �3) and (�3, 7).

10. Graph a line whose x-intercept is 5 and whose slope is ��35�. 10.

11. Write y � 4 � ��23�(x � 9) in standard form. 11.

12. Write the point-slope form of the equation for the line that 12.has x-intercept �3 and y-intercept �2.

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Chapter 5 Test, Form 3 (continued)

For Questions 13–20, write an equation in slope-intercept form of the linesatisfying the given conditions.

13. has y-intercept �8 and slope 3 13.

14. has slope �52� and passes through (4, �1) 14.

15. passes through (�3, 7) and (2, 4) 15.

16. is horizontal and passes through (�4, 6) 16.

17. is parallel to the y-axis and has an x-intercept of 3 17.

18. is perpendicular to 4y � 3x � 8 and passes through (�12, 7) 18.

19. is parallel to 3x � 5y � 7 and passes through (0, �6) 19.

20. is perpendicular to the y-axis and passes through (�2, 5) 20.

For Questions 21–23, use the data in the table.

21. Make a scatter plot relating the verbal scores and the 21.math scores.

22. Does the scatter plot in Question 21 show a positive, a 22.negative, or no correlation? What does that relationship represent?

23. Write the equation for a line of fit. Predict the 23.corresponding math score for a verbal score of 445.

24. A rental car company charges $52.99 per day, including 200 24.free kilometers. There is a charge of $0.12/km for additional kilometers. Write a linear equation that models this situation.

25. Write the slope-intercept form of y � 3 � �0.5(x � 10). 25.

Bonus The area of a circle varies directly as the square of the B:radius. If the radius is tripled, by what factor will the area increase?

Verbal Score

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500

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State Graduation Scores

Year Verbal Score Math Score1970 460 488

1980 424 466

1990 410 463

2000 420 460

Chapter 5 Open-Ended Assessment


Demonstrate your knowledge by giving a clear, concise solutionto each problem. Be sure to include all relevant drawings andjustify your answers. You may show your solution in more thanone way or investigate beyond the requirements of the problem.

1. Draw a line on a coordinate plane so that you can determine atleast two points on the graph.a. Describe how you would determine the slope of the graph and

justify the slope you found.b. Explain how you could use the slope to write various forms

of the equation of that line. Then write three forms of the equation.

2. You are told that a line passes through (�2, 3).a. Discuss what other information you would need to graph this

line.b. Then describe how you would use that information to graph

the line and write its equation.

3. Refer to the scatter plot at the right.a. Describe the pattern of points in the

scatter plot and the relationship between x and y.

b. Give at least two examples of real-life situations that, if graphed, would result in a correlation like the one shown in this scatter plot.

c. Add a scale and heading to each axis. Then write an equationthat would model the points represented by this plot.

4. The table gives the life expectancy of a child born in the United States in a given year.a. Make a scatter plot of the data.b. Can you use the data to claim

that the increase in life expectancy is due to improved health care? Explain your response.

c. Use the data to predict the life expectancy of a baby born in 2000. Explain how you determined your answer.

Source: National Center for Health Statistics

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Years of Life Expected at Birth

Year ofBirth

Life Expectancy(years)

1920 54.1

1930 59.7

1940 62.9

1950 68.2

1960 69.7

1970 70.8

1980 73.7

1985 74.7

1990 75.4

1995 75.8


Chapter 5 Vocabulary Test/Review

Choose from the terms above to complete each sentence.

1. If two lines have slopes that are negative reciprocals of each other,

then they are . If they have slopes that

are the same, then they are .

2. In the equation, y � kx, k represents the .

3. A graph of data points is sometimes called a .

4. Several graphs who have one or more common characteristics form a

.

5. Earning $7.50 per hour is an example of a .

6. The leftmost data point in a set is (3, 27) and the rightmost point is (12, 13). If you use a linear prediction equation to find thecorresponding y value for x � 10, you are using a method called

.

7. The ratio of the rise to the run or the ratio of the change in the y-coordinates to the change in the x-coordinates are definitions of

.

8. The equation y � �3x � 12 is written in form.

9. The equation y � 6 � 2(x � 4) is written in form.

10. The equation 3x � y � 12 is written in form.

In your own words—Define each term.

11. line of fit

12. linear extrapolation

best-fit lineconstant of variationdirect variationfamily of graphslinear extrapolation

linear interpolationline of fitnegative correlationparallel linesperpendicular lines

point-slope formpositive correlationrate of changescatter plot

slopeslope-intercept formstandard form

NAME DATE PERIOD

SCORE 55

Chapter 5 Quiz (Lessons 5–1 and 5–2)

55


Determine the slope of the line passing through each pair of points.

1. (5, 8) and (�4, 6) 1.

2. (9, 4) and (5, �3) 2.

3. (�3, 10) and (�3, 6) 3.

4. In 1996, there were approximately 275 students in the 4.Delaware High School band. In 2002, that number increased to 305. Find the annual rate of change in the number of students in the band.

5. Chris’s wages vary directly as the time she works. If her 5.wages for 20 hours are $150, what are her wages for 38 hours?

NAME DATE PERIOD

SCORE


Write the slope-intercept form of the equation for each situation.

1. slope: �14�, y-intercept: �5 1.

2. line passing through (9, 2) and (�2, 6) 2.

3. Graph 4x � 3y � 12. 3.

4. Write a linear equation in slope-intercept form to model a tree 4 feet tall that grows 3 inches per year. 4.

5. STANDARDIZED TEST PRACTICE The table of ordered pairs shows the coordinates of the two points on the graph of a function. Which equation describes the function?

A. y � �2x � 1 B. y � �12�x � 1

C. y � ��12�x � 1 D. y � ��

12�x � 1 5.

y

xO

NAME DATE PERIOD

SCORE 55

Ass

essm

ent

x y

�2 2

4 �1


1. Write the point-slope form of an equation for a line passing 1.

through (3, 6) with slope m � ��13�.

2. Write y � 9 � �(x � 2) in slope-intercept form. 2.

3. Write the point-slope form of an equation for the horizontal 3.line that passes through (�4, �1).

4. Write the slope-intercept form of an equation for the line 4.that passes through (5, 3) and is parallel to x � 3y � 6.

5. Write the slope-intercept form of an equation for the line 5.that passes through (0, 3) and is perpendicular to 9x � 4y � �8.

Chapter 5 Quiz (Lesson 5–7)

1. Use the data in the table to make a scatter plot relating 1–2.age to median income.

2. Draw a fit line for the scatter plot.

3. Do the data show a positive or negative relationship? What 3.does this relationship mean?

4. Write the slope-intercept form of an equation for a line of fit. 4.

5. Use the line of fit to predict the median income for someone 5.32 years old.

Age

Med

ian

Inco

me

($10

00)

16

19

22

25

28

31

26 27 28 29 30

NAME DATE PERIOD

SCORE


55

NAME DATE PERIOD

SCORE

55

Age 26 27 28 29 30

Median Income($1000) 16.8 19.1 23.3 25.8 33.9

Chapter 5 Mid-Chapter Test (Lessons 5–1 through 5–4)


Write the letter for the correct answer in the blank at the right of each question.

1. Find the slope of the line through (6, �7) and (4, �8).

A. ��12� B. 2 C. �

12� D. �2 1.

2. Find the slope of the line through (0, 5) and (5, 5).A. 0 B. 1 C. 2 D. no slope 2.

3. In 1999, 96.60 quadrillion Btu (British thermal units) of energy were consumed in the United States. In 1995, 90.86 quadrillion Btu were consumed. Which of the following is the rate of change in consumption from 1995 to 1999?A. 1.44 quadrillion btu per yearB. 5.74 quadrillion btu per yearC. 0.69 years per quadrillion btuD. 0.57 quadrillion btu per year 3.

4. The total price of a bag of peaches varies directly with the cost per pound.If 3 pounds of peaches cost $3.60, how much would 5.5 pounds cost?A. $1.20 B. $6.60 C. $6.00 D. $1.96 4.

5. Which is the slope-intercept form of an equation for the line containing (0, �3) with slope �1?A. y � �x � 3 B. y � �3x � 1 C. y � x � 3 D. x � �3y � 1 5.

For Questions 6–8, write an equation in slope-intercept form of the line satisfying the given conditions.

6. has y-intercept 5 and slope ��34� 6.

7. passes through (4, 2) and (0, �2) 7.

8. has slope �3 and passes through (2, �4) 8.

For Questions 9 and 10, use the graph at the right.

9. What is the slope of the line shown 9.in the graph?

10. What is the equation of the line 10.shown in the graph?

Part II

Part I

NAME DATE PERIOD

SCORE 55

Ass

essm

ent

y

xO

P (2, 0)


Chapter 5 Cumulative Review (Chapters 1–5)

1. Write 2 � r � r � s � s using exponents. (Lesson 1-1) 1.

2. Evaluate 2xy � y2 if x � 6 and y � 12. (Lesson 1-2) 2.

Simplify each expression. (Lessons 2-3 through 2-5)

3. 4�78� � 2�

58� 4. �

38� � 2�1

78�

5. ��23� � �

34� 6. �3.9 � (�2.5) � (�8.7)

7. 4(2y � y) � 6(4y � 3y) 8. �12a��618b

�

For Questions 9–11, solve each equation. (Lessons 3-2 through 3-4)

9. 13 � m � 21 9.

10. �34�x � �

23� 10.

11. 4x � 12 � �16 11.

12. Solve x � 2y � 12 if the domain is {�3, �1, 0, 2, 5}. 12.(Lesson 4-4)

13. Determine whether {(1, 4), (2, 6), (3, 7), (4, 4)} is a function, 13.and explain your reasoning. (Lesson 4-6)

14. Write an equation for the relationship between the variables 14.in the chart. (Lesson 4-8)

15. Determine the slope of the line passing through (2, 7) and 15.(�5, 2). (Lesson 5-1)

16. Write an equation in slope-intercept form for the line 16.passing through (2, 6) with slope �3. (Lesson 5-3)

17. Write an equation for the line passing through (�6, 5) and 17.(�6, �4). (Lesson 5-4)

18. Write the slope-intercept form of an equation for the line 18.that is parallel to 5x � 3y � 1 and passes through (0, �4).(Lesson 5-6)

NAME DATE PERIOD

55

3.

4.

5.

6.

7.

8.

x 0 2 4 6

y 2 5 8 11


1. If a � 2, b � 6, and c � 4, then �(4ba

��

cb)2

� � ? (Lesson 1-2)

A. 4 B. 0.4 C. 40 D. 0.04 1.

2. If 4 � 7 � 6 � 4 � 7 � 6 � n, what is the value of n? (Lesson 1-4)

E. 0 F. 1 G. 4 H. 6 2.

3. Lynn has 4 more books than José. If Lynn gives José 6 of her books, how many more will José have than Lynn? (Lesson 2-3)

A. 2 B. 4 C. 8 D. 10 3.

4. If x � �1264�

, which value of x does NOT form a proportion? (Lesson 2-6)

E. �23� F. �

34� G. �

1128�

H. �3428�

4.

5. Two-thirds of a number added to itself is 20. What is the number?(Lesson 3-1)

A. 12 B. 13 C. 30 D. 33 5.

6. 16% of 980 is 9.8% of what number? (Lesson 3-5)

E. 1.6 F. 16 G. 160 H. 1600 6.

7. For what value(s) of r is 3r � 6 � 7 � 3r? (Lesson 3-7)

A. all numbers B. all negative integersC. 0 D. no values of r 7.

8. The range of a relation includes the integers �4x

�, �5x

�, and �8x

�.

What could be a value for x in the domain? (Lesson 4-3)

E. 20 F. 30 G. 32 H. 40 8.

9. A line with a slope of �1 passes through points at (2, 3) and (5, y). Find the value of y. (Lesson 5-1)

A. �6 B. �3 C. 0 D. 6 9.

10. If a line passes through (0, �6) and has a slope of �3, what is an equation for the line? (Lesson 5-4)

E. y � �6x � 3 F. x � �6y � 3G. y � �3x � 6 H. x � �3y � 6 10. HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

NAME DATE PERIOD

55

Ass

essm

ent

Standardized Test Practice (Chapters 1–5)

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.


Standardized Test Practice (continued)

11. If x2 � 16 and y2 � 4, what is the greatest 11. 12.possible value of (x � y)2? (Lesson 2-8)

12. If �x � 22x � 3x� � 6, x � ? (Lesson 3-4)

13. The formula for the volume of a rectangular 13. 14.solid is V � Bh. A packing crate has a height of 4.5 inches and a base area of 18.2 square inches. What is the volume of the crate in cubic inches? (Lesson 3-8)

14. Find the slope of a line parallel to 2y � x � 6.(Lesson 5-6)

Column A Column B

15.

On the number line above, the marks are equally spaced.

15.

(Lesson 2-1)

16. 3x � 5 � 20

16.

(Lesson 3-4)

DCBA406x

DCBA�1377�x

13

12

x

Part 3: Quantitative Comparison

Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

Part 2: Grid In

Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.

NAME DATE PERIOD

55

NAME DATE PERIOD NAME DATE PERIOD

A

D

C

B

Standardized Test PracticeStudent Record Sheet (Use with pages 314–315 of the Student Edition.)

© Glencoe/McGraw-Hill A1 Glencoe Algebra 1

Select the best answer from the choices given and fill in the corresponding oval.

1 4 7

2 5 8

3 6 9

Solve the problem and write your answer in the blank.

For Questions 10, 12, and 14, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.

10 (grid in) 10 12 14

11

12 (grid in)

13

14 (grid in)

15

16

17

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

DCBADCBADCBA

DCBADCBADCBA

DCBADCBADCBA

NAME DATE PERIOD

55

An

swer

s

Part 2 Short Response/Grid InPart 2 Short Response/Grid In

Part 3 Extended ResponsePart 3 Extended Response

Part 1 Multiple ChoicePart 1 Multiple Choice

Record your answers for Questions 18–19 on the back of this paper.


Stu

dy G

uid

e a

nd I

nte

rven

tion

Slo

pe

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

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IOD

____

_

5-1

5-1

©G

lenc

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1G

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lgeb

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Lesson 5-1

Fin

d S

lop

e

Slo

pe

of

a L

ine

m�

or m

�,

whe

re (

x 1,

y 1)

and

(x2,

y2)

are

the

coo

rdin

ates

of a

ny t

wo

poin

ts o

n a

nonv

ertic

al li

ne

y 2�

y 1� x 2

�x 1

rise

� run

Fin

d t

he

slop

e of

th

eli

ne

that

pas

ses

thro

ugh

(�

3,5)

and

(4,

�2)

.

Let

(�

3,5)

�(x

1,y 1

) an

d (4

,�2)

�(x

2,y 2

).

m�

Slo

pe f

orm

ula

�y 2

��

2, y

1�

5, x

2�

4, x

1�

�3

�S

impl

ify.

��

1

�7

�7�

2 �

5�

�4

�(�

3)

y 2�

y 1� x

2�

x 1

Fin

d t

he

valu

e of

rso

th

at

the

lin

e th

rou

gh (

10,r

) an

d (

3,4)

has

a

slop

e of

�.

m�

Slo

pe f

orm

ula

��

m�

�,

y 2�

4, y

1�

r, x

2�

3, x

1�

10

��

Sim

plify

.

�2(

�7)

�7(

4 �

r)C

ross

mul

tiply

.

14 �

28 �

7rD

istr

ibut

ive

Pro

pert

y

�14

��

7rS

ubtr

act

28 f

rom

eac

h si

de.

2 �

rD

ivid

e ea

ch s

ide

by �

7.

4 �

r�

�7

2 � 7

2 � 7

4 �

r� 3

�10

2 � 7

y 2�

y 1� x

2�

x 1

2 � 7

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

Fin

d t

he

slop

e of

th

e li

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts.

1.(4

,9),

(1,6

)1

2.(�

4,�

1),(

�2,

�5)

�2

3.(�

4,�

1),(

�4,

�5)

un

def

ined

4.(2

,1),

(8,9

)5.

(14,

�8)

,(7,

�6)

�6.

(4,�

3),(

8,�

3)0

7.(1

,�2)

,(6,

2)8.

(2,5

),(6

,2)

�9.

(4,3

.5),

(�4,

3.5)

0

Det

erm

ine

the

valu

e of

rso

th

e li

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts h

asth

e gi

ven

slo

pe.

10.(

6,8)

,(r,

�2)

,m�

1�

411

.(�

1,�

3),(

7,r)

,m�

312

.(2,

8),(

r,�

4) m

��

36

13.(

7,�

5),(

6,r)

,m�

0�

514

.(r,

4),(

7,1)

,m�

1115

.(7,

5),(

r,9)

,m�

6

16.(

10,r

),(3

,4),

m�

�17

.(10

,4),

(�2,

r),m

��

0.5

18.(

r,3)

,(7,

r),m

��

210

2

1 � 52 � 7

23 � 33 � 4

3 � 4

3 � 44 � 5

2 � 74 � 3

©G

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w-H

ill28

2G

lenc

oe A

lgeb

ra 1

Rat

e o

f C

han

ge

Th

e ra

teof

ch

ange

tell

s,on

ave

rage

,how

a q

uan

tity

is

chan

gin

g ov

erti

me.

Slo

pe d

escr

ibes

a r

ate

of c

han

ge.

POPU

LATI

ON

Th

e gr

aph

sh

ows

the

pop

ula

tion

gro

wth

in

Ch

ina.

a.F

ind

th

e ra

tes

of c

han

ge f

or 1

950–

1975

an

d f

or

1975

–200

0.

1950

–197

5:� �

or 0

.015

2

1975

–200

0:� �

or 0

.012

4

b.

Exp

lain

th

e m

ean

ing

of t

he

slop

e in

eac

h c

ase.

Fro

m 1

950–

1975

,th

e gr

owth

was

0.0

152

bill

ion

per

yea

r,or

15.

2 m

illi

on p

er y

ear.

Fro

m 1

975–

2000

,th

e gr

owth

was

0.0

124

bill

ion

per

yea

r,or

12.

4 m

illi

on p

er y

ear.

c.H

ow a

re t

he

dif

fere

nt

rate

s of

ch

ange

sh

own

on

th

e gr

aph

?T

her

e is

a g

reat

er v

erti

cal

chan

ge f

or 1

950–

1975

th

an f

or 1

975–

2000

.Th

eref

ore,

the

sect

ion

of

the

grap

h f

or 1

950–

1975

has

a s

teep

er s

lope

.

LON

GEV

ITY

Th

e gr

aph

sh

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the

pre

dic

ted

lif

e ex

pec

tan

cy f

or m

en a

nd

wom

en b

orn

in

a g

iven

yea

r.

1.F

ind

the

rate

s of

ch

ange

for

wom

en f

rom

200

0–20

25

and

2025

–205

0.0.

16/y

r,0.

12/y

r

2.F

ind

the

rate

s of

ch

ange

for

men

fro

m 2

000–

2025

an

d20

25–2

050.

0.16

/yr,

0.12

/yr

3.E

xpla

in t

he

mea

nin

g of

you

r re

sult

s in

Exe

rcis

es 1

an

d 2.

Bo

th m

en a

nd

wo

men

incr

ease

d t

hei

r lif

e ex

pec

tan

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t th

e sa

me

rate

s.

4.W

hat

pat

tern

do

you

see

in

th

e in

crea

se w

ith

eac

h

25-y

ear

peri

od?

Wh

ile li

fe e

xpec

tan

cy

incr

ease

s,it

do

es n

ot

incr

ease

at

a co

nst

ant

rate

.

5.M

ake

a pr

edic

tion

for

th

e li

fe e

xpec

tan

cy f

or 2

050–

2075

.Exp

lain

how

you

arr

ived

at

you

r pr

edic

tion

.S

amp

le a

nsw

er:

89 f

or

wo

men

an

d 8

3 fo

r m

en;

the

dec

reas

e in

rat

e fr

om

200

0–20

25 t

o 2

025–

2050

is 0

.04/

yr.I

f th

e d

ecre

ase

in t

he

rate

rem

ain

s th

e sa

me,

the

chan

ge

of

rate

fo

r 20

50–2

075

mig

ht

be

0.08

/yr

and

25(

0.08

) �

2 ye

ars

of

incr

ease

ove

r th

e 25

-yea

r sp

an.

Pre

dic

tin

g L

ife E

xp

ect

an

cy

Year

Bo

rn

Age

2000

Wo

men

Men

100 95 90 85 80 75 70 65

2050

*20

25*

*Est

imat

ed

Sour

ce: U

SA T

OD

AY8084

8178

74

87

0.31

�251.24

�0.

93�

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00 �

1975

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0.55

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1975

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in

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��

�ch

ange

in

tim

e

Po

pu

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on

Gro

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in

Ch

ina

Year

People (billions)

1950

1975

2000

2.0

1.5

1.0

0.5 0

2025

*

*Est

imat

ed

Sour

ce: U

nite

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tions

Pop

ulat

ion

Divis

ion

0.55

0.93

1.24

1.48

Stu

dy G

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e a

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nte

rven

tion

(c

onti

nued

)

Slo

pe

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-1

5-1

Exer

cises

Exer

cises

Exam

ple

Exam

ple

Answers (Lesson 5-1)


An

swer

s

Skil

ls P

ract

ice

Slo

pe

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-1

5-1

©G

lenc

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w-H

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3G

lenc

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lgeb

ra 1

Lesson 5-1

Fin

d t

he

slop

e of

th

e li

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts.

1.2.

3.

2�

3

4.(2

,5),

(3,6

)1

5.(6

,1),

(�6,

1)0

6.(4

,6),

(4,8

)u

nd

efin

ed7.

(5,2

),(5

,�2)

un

def

ined

8.(2

,5),

(�3,

�5)

29.

(9,8

),(7

,�8)

8

10.(

�5,

�8)

,(�

8,1)

�3

11.(

�3,

10),

(�3,

7)u

nd

efin

ed

12.(

17,1

8),(

18,1

7)�

113

.(�

6,�

4),(

4,1)

14.(

10,0

),(�

2,4)

�15

.(2,

�1)

,(�

8,�

2)

16.(

5,�

9),(

3,�

2)�

17.(

12,6

),(3

,�5)

18.(

�4,

5),(

�8,

�5)

19.(

�5,

6),(

7,�

8)�

Fin

d t

he

valu

e of

rso

th

e li

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts h

as t

he

give

n s

lop

e.

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r,3)

,(5,

9),m

�2

221

.(5,

9),(

r,�

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48

22.(

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23.(

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24.(

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,(r,

�5)

,m�

43

25.(

7,r)

,(4,

6),m

�0

6

3 � 41 � 2

7 � 65 � 2

11 � 97 � 2

1 � 101 � 3

1 � 2

1 � 3

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) ( 1, –

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y

O

( 0, 0

)( 3, 1

)

x

y

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, 1)

( 2, 5

)

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lenc

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cGra

w-H

ill28

4G

lenc

oe A

lgeb

ra 1

Fin

d t

he

slop

e of

th

e li

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts.

1.2.

3.

�3

0

4.(6

,3),

(7,�

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75.

(�9,

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,(�

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1

6.(6

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27.

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4,8)

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,(�

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un

def

ined

9.(5

,9),

(3,9

)0

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15,2

),(�

6,5)

�11

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8)

12.(

�2,

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8)13

.(12

,10)

,(12

,5)

un

def

ined

14.(

0.2,

�0.

9),(

0.5,

�0.

9)0

15. �

,�, �

�,

�

Fin

d t

he

valu

e of

rso

th

e li

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts h

as t

he

give

n s

lop

e.

16.(

�2,

r),(

6,7)

,m�

317

.(�

4,3)

,(r,

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�4

18.(

�3,

�4)

,(�

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,m�

�5

19.(

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r),(

1,3)

,m�

�4

20.(

1,4)

,(r,

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un

defi

ned

121

.(�

7,2)

,(�

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�5

7

22.(

r,7)

,(11

,8),

m�

�16

23.(

r,2)

,(5,

r),m

�0

2

24.R

OO

FIN

GT

he

pitc

hof

a r

oof

is t

he

nu

mbe

r of

fee

t th

e ro

of r

ises

for

eac

h 1

2 fe

eth

oriz

onta

lly.

If a

roo

f h

as a

pit

ch o

f 8,

wh

at i

s it

s sl

ope

expr

esse

d as

a p

osit

ive

nu

mbe

r?

25. S

ALE

SA

dai

ly n

ewsp

aper

had

12,

125

subs

crib

ers

wh

en i

t be

gan

pu

blic

atio

n.F

ive

year

sla

ter

it h

ad 1

0,10

0 su

bscr

iber

s.W

hat

is

the

aver

age

year

ly r

ate

of c

han

ge i

n t

he

nu

mbe

rof

su

bscr

iber

s fo

r th

e fi

ve-y

ear

peri

od?

�40

5 su

bsc

rib

ers

per

yea

r

2 � 3

1 � 5

7 � 69 � 2

1 � 41 � 2

1 � 42 � 3

1 � 34 � 3

7 � 3

13 � 9

1 � 51 � 7

4 � 5

( –2,

3)

( 3, 3

)

x

y O

( 3, 1

)

( –2,

–3)

x

y

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1, 0

)

( –2,

3)

x

y

OPra

ctic

e (

Ave

rag

e)

Slo

pe

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-1

5-1



Readin

g t

o L

earn

Math

em

ati

csS

lop

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-1

5-1

©G

lenc

oe/M

cGra

w-H

ill28

5G

lenc

oe A

lgeb

ra 1

Lesson 5-1

Pre-

Act

ivit

yW

hy

is s

lop

e im

por

tan

t in

arc

hit

ectu

re?

Rea

d th

e in

trod

uct

ion

to

Les

son

5-1

at

the

top

of p

age

256

in y

our

text

book

.Th

en c

ompl

ete

the

defi

nit

ion

of

slop

e an

d fi

ll i

n t

he

boxe

son

th

e gr

aph

wit

h t

he

wor

ds r

ise

and

run

.

slop

e �

In t

his

gra

ph,t

he

rise

is

un

its,

and

the

run

is

un

its.

Th

us,

the

slop

e of

th

is l

ine

is

or

.

Rea

din

g t

he

Less

on

1.D

escr

ibe

each

typ

e of

slo

pe a

nd

incl

ude

a s

ketc

h.

Typ

e o

f S

lop

eD

escr

ipti

on

of

Gra

ph

Ske

tch

posi

tive

Th

e g

rap

h r

ises

as

you

go

fro

m le

ft t

o

rig

ht.

nega

tive

Th

e g

rap

h f

alls

as

you

go

fro

m le

ft t

o

rig

ht.

zero

Th

e g

rap

h is

a h

ori

zon

tal l

ine.

unde

fined

Th

e g

rap

h is

a v

erti

cal l

ine.

2.D

escr

ibe

how

eac

h e

xpre

ssio

n i

s re

late

d to

slo

pe.

a.d

iffe

ren

ce o

f y-

coo

rdin

ates

div

ided

by

dif

fere

nce

of

corr

esp

on

din

g x

-co

ord

inat

es

b.

ho

w f

ar u

p o

r d

ow

n a

s co

mp

ared

to

ho

w f

ar le

ft o

r ri

gh

t

c.sl

op

e u

sed

as

rate

of

chan

ge

Hel

pin

g Y

ou

Rem

emb

er3.

Th

e w

ord

rise

is u

sual

ly a

ssoc

iate

d w

ith

goi

ng

up.

Som

etim

es g

oin

g fr

om o

ne

poin

t on

the

grap

h d

oes

not

in

volv

e a

rise

an

d a

run

bu

t a

fall

an

d a

run

.Des

crib

e h

ow y

ou c

ould

sele

ct p

oin

ts s

o th

at i

t is

alw

ays

a ri

se f

rom

th

e fi

rst

poin

t to

th

e se

con

d po

int.

Sam

ple

an

swer

:If

th

e sl

op

e is

neg

ativ

e,ch

oo

se t

he

seco

nd

po

int

so t

hat

its

x-co

ord

inat

e is

less

th

an t

hat

of

the

firs

t p

oin

t.

$52,

000

incr

ease

in

spe

ndi

ng

��

��

26 m

onth

s

rise

� run

y 2�

y 1� x 2

�x 1

x

y

O

x

y

O

x

y

O

x

y

O

3 � 53

un

its

� 5u

nit

s

53

rise

� run

x

y

O

rise

run

©G

lenc

oe/M

cGra

w-H

ill28

6G

lenc

oe A

lgeb

ra 1

Trea

sure

Hu

nt

wit

h S

lop

esU

sin

g th

e d

efin

itio

n o

f sl

ope,

dra

w l

ines

wit

h t

he

slop

es l

iste

d

bel

ow.A

cor

rect

sol

uti

on w

ill

trac

e th

e ro

ute

to

the

trea

sure

.

1.3

2.3.

�4.

0

5.1

6.�

17.

no

slop

e8.

9.10

.11

.�

12.

33 � 4

1 � 33 � 2

2 � 7

2 � 51 � 4

Star

t Her

e

Trea

sure

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-1

5-1



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

Slo

pe

and

Dir

ect V

aria

tio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-2

5-2

©G

lenc

oe/M

cGra

w-H

ill28

7G

lenc

oe A

lgeb

ra 1

Lesson 5-2

Dir

ect

Var

iati

on

A d

irec

t va

riat

ion

is d

escr

ibed

by

an e

quat

ion

of

the

form

y�

kx,

wh

ere

k�

0.W

e sa

y th

at y

var

ies

dir

ectl

y as

x.I

n t

he

equ

atio

n y

�kx

,kis

th

e co

nst

ant

of v

aria

tion

.

Nam

e th

e co

nst

ant

ofva

riat

ion

for

th

e eq

uat

ion

.Th

en f

ind

the

slop

e of

th

e li

ne

that

pas

ses

thro

ugh

th

e p

air

of p

oin

ts.

For

y�

x,th

e co

nst

ant

of v

aria

tion

is

.

m�

Slo

pe f

orm

ula

�(x

1, y

1) �

(0,

0),

(x2,

y2)

�(2

, 1)

�S

impl

ify.

Th

e sl

ope

is

.1 � 2

1 � 21 �

0� 2

�0

y 2�

y 1� x

2�

x 1

1 � 21 � 2

( 2, 1

)( 0

, 0)

x

y

Oy

� 1 2x

Su

pp

ose

yva

ries

dir

ectl

y as

x,a

nd

y�

30 w

hen

x�

5.

a.W

rite

a d

irec

t va

riat

ion

eq

uat

ion

that

rel

ates

xan

d y

.F

ind

the

valu

e of

k.

y�

kxD

irect

var

iatio

n eq

uatio

n

30 �

k(5)

Rep

lace

yw

ith 3

0 an

d x

with

5.

6 �

kD

ivid

e ea

ch s

ide

by 5

.

Th

eref

ore,

the

equ

atio

n i

s y

�6x

.

b.

Use

th

e d

irec

t va

riat

ion

eq

uat

ion

to

fin

d x

wh

en y

�18

.y

�6x

Dire

ct v

aria

tion

equa

tion

18 �

6xR

epla

ce y

with

18.

3 �

xD

ivid

e ea

ch s

ide

by 6

.

Th

eref

ore,

x�

3 w

hen

y�

18.

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

Nam

e th

e co

nst

ant

of v

aria

tion

for

eac

h e

qu

atio

n.T

hen

det

erm

ine

the

slop

e of

th

eli

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts.

1.2.

3.

�2;

�2

3;3

;

Wri

te a

dir

ect

vari

atio

n e

qu

atio

n t

hat

rel

ates

xto

y.A

ssu

me

that

yva

ries

dir

ectl

yas

x.T

hen

sol

ve.

4.If

y�

4 w

hen

x�

2,fi

nd

yw

hen

x�

16.

y�

2x;

325.

If y

�9

wh

en x

��

3,fi

nd

xw

hen

y�

6.y

��

3x;

�2

6.If

y�

�4.

8 w

hen

x�

�1.

6,fi

nd

x w

hen

y�

�24

.y

�3x

;�

87.

If y

�w

hen

x�

,fin

d x

wh

en y

�.

y�

2x;

3 � 323 � 16

1 � 81 � 4

3 � 23 � 2( –

2, –

3)

( 0, 0

)x

y O

y �

3 2x

( 1, 3

)

( 0, 0

)x

y

O

y �

3x

( –1,

2)

( 0, 0

)x

y

Oy

� –

2x

©G

lenc

oe/M

cGra

w-H

ill28

8G

lenc

oe A

lgeb

ra 1

Solv

e Pr

ob

lem

sT

he

dis

tan

ce f

orm

ula

d�

rtis

a d

irec

t va

riat

ion

equ

atio

n.I

n t

he

form

ula

,dis

tan

ce d

vari

es d

irec

tly

as t

ime

t,an

d th

e ra

te r

is t

he

con

stan

t of

var

iati

on.

TRA

VEL

A f

amil

y d

rove

th

eir

car

225

mil

es i

n 5

hou

rs.

a.W

rite

a d

irec

t va

riat

ion

eq

uat

ion

to

fin

d t

he

dis

tan

ce t

rave

led

for

an

y n

um

ber

of h

ours

.U

se g

iven

val

ues

for

dan

d t

to f

ind

r.d

�rt

Orig

inal

equ

atio

n

225

�r(

5)d

�22

5 an

d t�

5

45�

rD

ivid

e ea

ch s

ide

by 5

.

Th

eref

ore,

the

dire

ct v

aria

tion

equ

atio

n i

s d

�45

t.b

.G

rap

h t

he

equ

atio

n.

Th

e gr

aph

of

d�

45t

pass

es t

hro

ugh

th

e or

igin

wit

hsl

ope

45.

m�

✓C

HEC

K(5

,225

) li

es o

n t

he

grap

h.

c.E

stim

ate

how

man

y h

ours

it

wou

ld t

ake

the

fam

ily

to d

rive

360

mil

es.

d�

45t

Orig

inal

equ

atio

n

360

�45

tR

epla

ce d

with

360

.

t�

8D

ivid

e ea

ch s

ide

by 4

5.

Th

eref

ore,

it w

ill

take

8 h

ours

to

driv

e 36

0 m

iles

.

RET

AIL

Th

e to

tal

cost

Cof

bu

lk j

elly

bea

ns

is

$4.4

9 ti

mes

th

e n

um

ber

of

pou

nd

s p

.

1.W

rite

a d

irec

t va

riat

ion

equ

atio

n t

hat

rel

ates

th

e va

riab

les.

C�

4.49

p2.

Gra

ph t

he

equ

atio

n o

n t

he

grid

at

the

righ

t.

3.F

ind

the

cost

of

pou

nd

of je

lly

bean

s.$3

.37

CH

EMIS

TRY

Ch

arle

s’s

Law

sta

tes

that

,at

a co

nst

ant

pre

ssu

re,v

olu

me

of a

gas

Vva

ries

dir

ectl

y as

its

tem

per

atu

reT

.A v

olu

me

of 4

cu

bic

fee

t of

a c

erta

in g

as h

as a

tem

per

atu

reof

200

°(a

bso

lute

tem

per

atu

re).

V�

0.02

T4.

Wri

te a

dir

ect

vari

atio

n e

quat

ion

th

at r

elat

es t

he

vari

able

s.

5.G

raph

th

e eq

uat

ion

on

th

e gr

id a

t th

e ri

ght.

5 ft

3

6.F

ind

the

volu

me

of t

he

sam

e ga

s at

250

°(a

bsol

ute

tem

pera

ture

).

Ch

arl

es’

s La

w

Tem

per

atu

re (

�K)

Volume (cubic feet)

100

020

0T

V 4 3 2 1

3 � 4

Co

st o

f Je

lly B

ean

s

Wei

gh

t (p

ou

nd

s)

Cost (dollars)

20

4w

C

18.0

0

13.5

0

9.00

4.50

rise

� run

45 � 1

Au

tom

ob

ile T

rip

s

Tim

e (h

ou

rs)

Distance (miles)

10

23

45

67

8t

d

360

270

180 90

( 1, 4

5)

( 5, 2

25)

d �

45t

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

Slo

pe

and

Dir

ect V

aria

tio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-2

5-2

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Skil

ls P

ract

ice

Slo

pe

and

Dir

ect V

aria

tio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-2

5-2

©G

lenc

oe/M

cGra

w-H

ill28

9G

lenc

oe A

lgeb

ra 1

Lesson 5-2

Nam

e th

e co

nst

ant

of v

aria

tion

for

eac

h e

qu

atio

n.T

hen

det

erm

ine

the

slop

e of

th

eli

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts.

1.;

2.�

2;�

23.

�;

�

Gra

ph

eac

h e

qu

atio

n.

4.y

�3x

5.y

��

x6.

y�

x

Wri

te a

dir

ect

vari

atio

n e

qu

atio

n t

hat

rel

ates

xan

d y

.Ass

um

e th

at y

vari

esd

irec

tly

as x

.Th

en s

olve

.

7.If

y�

�8

wh

en x

��

2,fi

nd

x8.

If y

�45

wh

en x

�15

,fin

d x

wh

en y

�32

.y

�4x

;8

wh

en y

�15

.y

�3x

;5

9.If

y�

�4

wh

en x

�2,

fin

d y

10.I

f y

��

9 w

hen

x�

3,fi

nd

yw

hen

x�

�6.

y�

�2x

;12

wh

en x

��

5.y

��

3x;

15

11.I

f y

�4

wh

en x

�16

,fin

d y

12.I

f y

�12

wh

en x

�18

,fin

d x

wh

en x

�6.

y�

x;w

hen

y�

�16

.y

�x;

�24

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te a

dir

ect

vari

atio

n e

qu

atio

n t

hat

rel

ates

th

e va

riab

les.

Th

en g

rap

h t

he

equ

atio

n.

13. T

RA

VEL

Th

e to

tal

cost

Cof

gas

olin

e

14.S

HIP

PIN

GT

he

nu

mbe

r of

del

iver

ed t

oys

Tis

$1.

80 t

imes

th

e n

um

ber

of g

allo

ns

g.is

3 t

imes

th

e to

tal

nu

mbe

r of

cra

tes

c.

C�

1.80

gT

�3c

Toys

Sh

ipp

ed

Cra

tes

Toys

20

46

71

35

c

T

21 18 15 12 9 6 3

Gaso

lin

e C

ost

Gal

lon

s

Cost ($)

40

812

142

610

g

C 28 24 20 16 12 8 4

2 � 33 � 2

1 � 4

x

y

O

2 � 5

x

y

O

3 � 4

x

y

O

3 � 23 � 2( –

2, 3

)

( 0, 0

)x

y

O

y �

– 3 2x

( –1,

2)

( 0, 0

)x

y

O

y �

–2x

1 � 31 � 3

( 3, 1

)( 0

, 0)

x

y O

y �

1 3x

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Nam

e th

e co

nst

ant

of v

aria

tion

for

eac

h e

qu

atio

n.T

hen

det

erm

ine

the

slop

e of

th

eli

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts.

1.;

2.;

3.�

;�

Gra

ph

eac

h e

qu

atio

n.

4.y

��

2x5.

y�

x6.

y�

�x

Wri

te a

dir

ect

vari

atio

n e

qu

atio

n t

hat

rel

ates

xan

d y

.Ass

um

e th

at y

vari

esd

irec

tly

as x

.Th

en s

olve

.

7.If

y�

7.5

wh

en x

�0.

5,fi

nd

yw

hen

x�

�0.

3.y

�15

x;�

4.5

8.If

y�

80 w

hen

x�

32,f

ind

xw

hen

y�

100.

y�

2.5x

;40

9.If

y�

wh

en x

�24

,fin

d y

wh

en x

�12

.y

�x;

Wri

te a

dir

ect

vari

atio

n e

qu

atio

n t

hat

rel

ates

th

e va

riab

les.

Th

en g

rap

h t

he

equ

atio

n.

10. M

EASU

RE

Th

e w

idth

Wof

a

11.T

ICK

ETS

Th

e to

tal

cost

Cof

tic

kets

is

rect

angl

e is

tw

o th

irds

of

the

len

gth

�.

$4.5

0 ti

mes

th

e n

um

ber

of t

icke

ts t

.

W�

�C

�4.

50t

12.P

RO

DU

CE

Th

e co

st o

f ba

nan

as v

arie

s di

rect

ly w

ith

th

eir

wei

ght.

Mig

uel

bou

ght

3po

un

ds o

f ba

nan

as f

or $

1.12

.Wri

te a

n e

quat

ion

th

at r

elat

es t

he

cost

of

the

ban

anas

to t

hei

r w

eigh

t.T

hen

fin

d th

e co

st o

f 4

pou

nds

of

ban

anas

.C

�0.

32p

;$1

.36

1 � 4

1 � 2

Co

st o

f Ti

ckets

Tick

ets

Cost ($)

20

46

13

5t

C 25 20 15 10 5

Rect

an

gle

Dim

en

sio

ns

Len

gth

Width

40

812

26

10�

W 10 8 6 4 2

2 � 3

3 � 81 � 32

3 � 4

x

y

O

5 � 3

x

y

O

6 � 5

x

y

O

5 � 25 � 2

( –2,

5)

( 0, 0

)x

y

O

y �

� 5 2x

4 � 34 � 3

( 3, 4

)

( 0, 0

)x

y O

y �

4 3x

3 � 43 � 4

( 4, 3

)

( 0, 0

)x

y O

y �

3 4x

Pra

ctic

e (

Ave

rag

e)

Slo

pe

and

Dir

ect V

aria

tio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-2

5-2



An

swer

s

Readin

g t

o L

earn

Math

em

ati

csS

lop

e an

d D

irec

t Var

iati

on

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-2

5-2

©G

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1G

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Lesson 5-2

Pre-

Act

ivit

yH

ow i

s sl

ope

rela

ted

to

you

r sh

ower

?

Rea

d th

e in

trod

uct

ion

to

Les

son

5-2

at

the

top

of p

age

264

in y

our

text

book

.

•H

ow d

o th

e n

um

bers

in

th

e ta

ble

rela

te t

o th

e gr

aph

sh

own

?T

hey

are

th

e co

ord

inat

es o

f th

e p

oin

ts o

n t

he

gra

ph

.

•T

hin

k ab

out

the

firs

t se

nte

nce

.Wh

at d

oes

it m

ean

to

say

that

a s

tan

dard

show

erh

ead

use

s ab

out

6 ga

llon

s of

wat

er p

er m

inu

te?

Sam

ple

an

swer

:F

or

each

min

ute

th

e sh

ow

er r

un

s,6

gal

lon

so

f w

ater

co

me

ou

t.S

o,i

f th

e sh

ow

er r

an 1

0 m

inu

tes,

that

wo

uld

be

60 g

allo

ns.

Rea

din

g t

he

Less

on

1.W

hat

is

the

form

of

a di

rect

var

iati

on e

quat

ion

?y

�kx

2.H

ow i

s th

e co

nst

ant

of v

aria

tion

rel

ated

to

slop

e?T

he

con

stan

t o

f va

riat

ion

has

the

sam

e va

lue

as t

he

slo

pe

of

the

gra

ph

of

the

equ

atio

n.

3.T

he

expr

essi

on “

yva

ries

dir

ectl

y as

x”

can

be

wri

tten

as

the

equ

atio

n y

�kx

.How

wou

ldyo

u w

rite

an

equ

atio

n f

or “

wva

ries

dir

ectl

y as

th

e sq

uar

e of

t”?

w�

kt2

4.F

or e

ach

sit

uat

ion

,wri

te a

n e

quat

ion

wit

h t

he

prop

er c

onst

ant

of v

aria

tion

.

a.T

he

dist

ance

dva

ries

dir

ectl

y as

tim

e t,

and

a ch

eeta

h c

an t

rave

l 88

fee

t in

1 s

econ

d.d

�88

t

b.

Th

e pe

rim

eter

pof

a p

enta

gon

wit

h a

ll s

ides

of

equ

al l

engt

h v

arie

s di

rect

ly a

s th

ele

ngt

h s

of a

sid

e of

th

e pe

nta

gon

.A p

enta

gon

has

5 s

ides

.p

�5s

c.T

he

wag

es W

earn

ed b

y an

em

ploy

ee v

ary

dire

ctly

wit

h t

he

nu

mbe

r of

hou

rs h

that

are

wor

ked.

En

riqu

e ea

rned

$17

2.50

for

23

hou

rs o

f w

ork.

W�

$7.5

0h

Hel

pin

g Y

ou

Rem

emb

er

5.L

ook

up

the

wor

d co

nst

ant

in a

dic

tion

ary.

How

doe

s th

is d

efin

itio

n r

elat

e to

th

e te

rmco

nst

ant

of v

aria

tion

?S

amp

le a

nsw

er:

So

met

hin

g u

nch

ang

ing

;th

e co

nst

ant

of

vari

atio

n r

elat

es x

and

yin

th

e sa

me

valu

e ev

ery

tim

e,an

d t

hat

rela

tio

nsh

ip n

ever

ch

ang

es.

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lenc

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ill29

2G

lenc

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ra 1

nth

Po

wer

Var

iati

on

An

equa

tion

of

the

form

y�

kxn ,

whe

re k

�0,

desc

ribe

s an

nth

pow

erva

riat

ion.

The

var

iabl

e n

can

be r

epla

ced

by 2

to

indi

cate

the

sec

ond

pow

erof

x(t

he s

quar

e of

x)

or b

y 3

to in

dica

te t

he t

hird

pow

er o

f x

(the

cub

e of

x).

Ass

um

e th

at t

he

wei

ght

of a

per

son

of

aver

age

buil

d va

ries

dir

ectl

y as

th

ecu

be o

f th

at p

erso

n’s

hei

ght.

Th

e eq

uat

ion

of

vari

atio

n h

as t

he

form

w

�kh

3 .

The

wei

ght

that

a p

erso

n’s

legs

wil

l sup

port

is p

ropo

rtio

nal t

o th

e cr

oss-

sect

iona

l are

a of

the

leg

bone

s.T

his

area

var

ies

dire

ctly

as

the

squa

reof

the

per

son’

s he

ight

.The

equ

atio

n of

var

iati

on h

as t

he f

orm

s�

kh2 .

An

swer

eac

h q

ues

tion

.

1.F

or a

per

son

6 f

eet

tall

wh

o w

eigh

s 20

0 po

un

ds,f

ind

a va

lue

for

kin

th

e eq

uat

ion

w�

kh3 .

k�

0.93

2.U

se y

our

answ

er f

rom

Exe

rcis

e 1

to p

redi

ct t

he

wei

ght

of a

per

son

wh

o is

5 f

eet

tall

.ab

ou

t 11

6 p

ou

nd

s

3.F

ind

the

valu

e fo

r k

in t

he

equ

atio

n w

�kh

3fo

r a

baby

wh

o is

20

inch

es

lon

g an

d w

eigh

s 6

pou

nds

.

k�

1.29

6 fo

r h

�ft

4.H

ow d

oes

you

r an

swer

to

Exe

rcis

e 3

dem

onst

rate

th

at a

bab

y is

si

gnif

ican

tly

fatt

er i

n p

ropo

rtio

n t

o it

s h

eigh

t th

an a

n a

dult

?

kh

as a

gre

ater

val

ue.

5.F

or a

per

son

6 f

eet

tall

wh

o w

eigh

s 20

0 po

un

ds,f

ind

a va

lue

for

kin

th

e eq

uat

ion

s�

kh2 .

k�

5.56

6.F

or a

bab

y w

ho

is 2

0 in

ches

lon

g an

d w

eigh

s 6

pou

nds

,fin

d an

“in

fan

t va

lue”

for

kin

th

e eq

uat

ion

s�

kh2 .

k�

2.16

fo

r h

�ft

7.A

ccor

din

g to

th

e ad

ult

equ

atio

n y

ou f

oun

d (E

xerc

ise

1),h

ow m

uch

w

ould

an

im

agin

ary

gian

t 20

fee

t ta

ll w

eigh

?

7440

po

un

ds

8.A

ccor

din

g to

th

e ad

ult

equ

atio

n f

or w

eigh

t su

ppor

ted

(Exe

rcis

e 5)

,how

m

uch

wei

ght

cou

ld a

20-

foot

tal

l gi

ant’s

leg

s ac

tual

ly s

upp

ort?

on

ly 2

224

po

un

ds

9.W

hat

can

you

con

clu

de f

rom

Exe

rcis

es 7

an

d 8?

An

swer

s w

ill v

ary.

Fo

r ex

amp

le,b

on

e st

ren

gth

lim

its

the

size

hu

man

sca

n a

ttai

n.

5 � 3

5 � 3

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-2

5-2



Stu

dy G

uid

e a

nd I

nte

rven

tion

Slo

pe-

Inte

rcep

t F

orm

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-3

5-3

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3G

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Lesson 5-3

Slo

pe-

Inte

rcep

t Fo

rm

Slo

pe-

Inte

rcep

t F

orm

y�

mx

�b,

whe

re m

is t

he g

iven

slo

pe a

nd b

is t

he y

-inte

rcep

t

Wri

te a

n e

qu

atio

n o

f th

e li

ne

wh

ose

slop

e is

�4

and

wh

ose

y-in

terc

ept

is 3

.y

�m

x�

bS

lope

-inte

rcep

t fo

rm

y�

�4x

�3

Rep

lace

mw

ith �

4 an

d b

with

3.

Gra

ph

3x

�4y

�8.

3x�

4y�

8O

rigin

al e

quat

ion

�4y

��

3x�

8S

ubtr

act

3xfr

om e

ach

side

.

�D

ivid

e ea

ch s

ide

by �

4.

y�

x�

2S

impl

ify.

Th

e y-

inte

rcep

t of

y�

x�

2 is

�2

and

the

slop

e is

.S

o gr

aph

th

e po

int

(0,�

2).F

rom

this

poi

nt,

mov

e u

p 3

un

its

and

righ

t 4

un

its.

Dra

w a

lin

e pa

ssin

g th

rou

gh b

oth

poi

nts

.

Wri

te a

n e

qu

atio

n o

f th

e li

ne

wit

h t

he

give

n s

lop

e an

d y

-in

terc

ept.

1.sl

ope:

8,y-

inte

rcep

t �

32.

slop

e:�

2,y-

inte

rcep

t �

13.

slop

e:�

1,y-

inte

rcep

t �

7y

�8x

�3

y�

�2x

�1

y�

�x

�7

Wri

te a

n e

qu

atio

n o

f th

e li

ne

show

n i

n e

ach

gra

ph

.

4.5.

6.

y�

2x�

2y

��

x�

3y

�x

�5

Gra

ph

eac

h e

qu

atio

n.

7.y

�2x

�1

8.y

��

3x�

29.

y�

�x

�1

x

y

Ox

y

Ox

y

O

3 � 4

( 4, –

2)

( 0, –

5)

xy

O

( 3, 0

)

( 0, 3

)

x

y

O( 0

, –2)

( 1, 0

)x

y

O

3 � 43 � 4

3 � 4�3x

�8

��

�4

�4y

� �4

( 0, –

2)

( 4, 1

)

x

y

O

3x �

4y

� 8

Exam

ple

1Ex

ampl

e 1

Exam

ple

2Ex

ampl

e 2

Exer

cises

Exer

cises

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w-H

ill29

4G

lenc

oe A

lgeb

ra 1

Mo

del

Rea

l-W

orl

d D

ata

MED

IAS

ince

199

7,th

e n

um

ber

of

cab

le T

V s

yste

ms

has

dec

reas

edb

y an

ave

rage

rat

e of

121

sys

tem

s p

er y

ear.

Th

ere

wer

e 10

,943

sys

tem

s in

199

7.

a.W

rite

a l

inea

r eq

uat

ion

to

fin

d t

he

aver

age

nu

mb

er o

f ca

ble

sys

tem

s in

an

y ye

araf

ter

1997

.T

he

rate

of

chan

ge i

s �

121

syst

ems

per

year

.In

th

e fi

rst

year

,th

e n

um

ber

of s

yste

ms

was

10,9

43.L

et N

�th

e nu

mbe

r of

cab

le T

V s

yste

ms.

Let

x�

the

num

ber

of y

ears

aft

er 1

997.

An

equa

tion

isN

��

121x

�10

,943

.

b.

Gra

ph

th

e eq

uat

ion

.T

he

grap

h o

f N

��

121x

�10

,943

is

a li

ne

that

pas

ses

thro

ugh

th

e po

int

at (

0,10

,943

) an

d h

as a

slo

pe o

f �

121.

c.F

ind

th

e ap

pro

xim

ate

nu

mb

er o

f ca

ble

TV

sy

stem

s in

200

0.N

��

121x

�10

,943

Orig

inal

equ

atio

n

N�

�12

1(3)

�10

,943

Rep

lace

xw

ith 3

.

N�

10,5

80S

impl

ify.

Th

ere

wer

e ab

out

10,5

80 c

able

TV

sys

tem

s in

200

0.

ENTE

RTA

INM

ENT

In 1

995,

65.7

% o

f al

l h

ouse

hol

ds

wit

h T

V’s

in

th

e U

.S.s

ub

scri

bed

to

cab

le T

V.B

etw

een

199

5an

d 1

999,

the

per

cen

t in

crea

sed

by

abou

t 0.

6% e

ach

yea

r.

1.W

rite

an

equ

atio

n t

o fi

nd

the

perc

ent

Pof

hou

seh

olds

th

atsu

bscr

ibed

to

cabl

e T

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ind

the

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ent

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ibed

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cabl

e T

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n 1

999.

68.1

%

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LATI

ON

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e p

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on o

f th

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tate

s is

p

roje

cted

to

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300

mil

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the

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etw

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20

10 a

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205

0,th

e p

opu

lati

on i

s ex

pec

ted

to

incr

ease

by

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t 2.

5 m

illi

on p

er y

ear.

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rite

an

equ

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n t

o fi

nd

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lati

on P

in a

ny

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raph

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e eq

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t th

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ind

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n 2

050.

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ut

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ject

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pu

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nce

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Population (millions)

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400

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360

340

320

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ce: T

he W

orld

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anac

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nce

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ce: T

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nce

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Number of Cable TV Systems

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)

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____

____

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5-3

Exam

ple

Exam

ple

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cises

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swer

s

Skil

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ract

ice

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____

____

____

____

____

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ITIN

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la h

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es p

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onth

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13.W

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ind

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er 5

mon

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85

Carl

a’s

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Pages Written

20

46

13

5m

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100 80 60 40 20

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5-3

5-3



Readin

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o L

earn

Math

em

ati

csS

lop

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Fo

rm

NA

ME

____

____

____

____

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____

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____

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AT

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ER

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5-3

5-3

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7G

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Lesson 5-3

Pre-

Act

ivit

yH

ow i

s a

y-in

terc

ept

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ted

to

a fl

at f

ee?

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d th

e in

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uct

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Les

son

5-3

at

the

top

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age

272

in y

our

text

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.

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hat

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nt

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at t

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on

1.F

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in t

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y�

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hat

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def

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d t

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th

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wh

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es t

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y-ax

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4.R

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out

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a r

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um

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ven

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he

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t at

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ate

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row

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eeks

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.Bel

ow t

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equ

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ill

in a

ny

valu

es y

ou k

now

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d pu

t a

ques

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mar

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the

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e an

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the

nu

mb

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.

c.U

se t

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u d

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wh

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Rem

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5.O

ne

way

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hin

g is

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expl

ain

it

to a

not

her

per

son

.Wri

te h

ow y

ou w

ould

expl

ain

to

som

eon

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oces

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r u

sin

g th

e y-

inte

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d sl

ope

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raph

a l

inea

req

uat

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.O

n t

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y-ax

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lot

the

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Th

en u

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rise

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rate

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t at

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6

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8G

lenc

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Rel

atin

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lop

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Fo

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Sta

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rms

You

hav

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arn

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fin

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erm

s of

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.

An

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lin

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C � BA � B

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rise

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En

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t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

____

_

5-3

5-3



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

Wri

tin

g E

qu

atio

ns

in S

lop

e-In

terc

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Fo

rm

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

____

_

5-4

5-4

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lenc

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9G

lenc

oe A

lgeb

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Lesson 5-4

Wri

te a

n E

qu

atio

n G

iven

th

e Sl

op

e an

d O

ne

Poin

t

Wri

te a

n e

qu

atio

n o

fa

lin

e th

at p

asse

s th

rou

gh (

�4,

2)w

ith

slo

pe

3.

Th

e li

ne

has

slo

pe 3

.To

fin

d th

e y-

inte

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plac

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wit

h 3

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d (x

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wit

h (

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2) i

n t

he

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ept

form

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hen

sol

ve f

or b

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x�

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lope

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rm

2 �

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bm

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y�

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nd x

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tiply

.

14 �

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dd 1

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eref

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the

equ

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n i

s y

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.

Wri

te a

n e

qu

atio

n o

f th

e li

ne

that

pas

ses

thro

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(�

2,�

1) w

ith

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pe

.

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e li

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pe

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lace

mw

ith

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d (x

,y)

wit

h (

�2,

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in

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eref

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�x

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1 � 21 � 4

1 � 2

1 � 2

1 � 2

1 � 4

1 � 4

1 � 41 � 4

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ple1

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ple1

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ple2

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ple2

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cises

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cises

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n e

qu

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5-4

5-4



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5-4

5-4



Stu

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5-5

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Wri

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NA

ME

____

____

____

____

____

____

____

____

____

____

____

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____

____

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ER

IOD

____

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5-5

5-5



Readin

g t

o L

earn

Math

em

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csW

riti

ng

Eq

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s in

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Fo

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____

____

____

____

____

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____

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Lesson 5-5

Pre-

Act

ivit

yH

ow c

an y

ou u

se t

he

slop

e fo

rmu

la t

o w

rite

an

eq

uat

ion

of

a li

ne?

Rea

d th

e in

trod

uct

ion

to

Les

son

5-5

at

the

top

of p

age

286

in y

our

text

book

.

Not

e th

at i

n t

he

fin

al e

quat

ion

th

ere

is a

val

ue

subt

ract

ed f

rom

xan

d fr

om y

.Wh

at a

re t

hes

e va

lues

?T

he

valu

e su

btr

acte

d f

rom

xis

th

e x-

coo

rdin

ate

of

the

giv

enp

oin

t.T

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valu

e su

btr

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d f

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th

e y-

coo

rdin

ate

of

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din

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Less

on

1.In

th

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�y 1

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x 1),

wh

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o x 1

and

y 1re

pres

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x 1an

d y

1re

pre

sen

t th

e co

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inat

es o

f an

y g

iven

po

int

on

th

e g

rap

h

of

the

line.

2.C

ompl

ete

the

char

t be

low

by

list

ing

thre

e fo

rms

of e

quat

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s.T

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wri

te t

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form

ula

for

each

for

m.F

inal

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rite

th

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exam

ples

of

equ

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ns

in t

hos

e fo

rms.

Sam

ple

exa

mp

les

are

giv

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qu

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15

3.R

efer

to

Exa

mpl

e 5

on p

age

288

of y

our

text

book

.Wh

at d

o yo

u t

hin

k th

e h

ypot

enu

seof

ari

ght

tria

ngl

e is

?S

amp

le a

nsw

ers:

Th

e hy

po

ten

use

is t

he

lon

ges

t si

de

of

the

rig

ht

tria

ng

le.T

he

hyp

ote

nu

se is

th

e si

de

op

po

site

th

e ri

gh

t an

gle

ina

rig

ht

tria

ng

le.

Hel

pin

g Y

ou

Rem

emb

er

4.S

upp

ose

you

cou

ld n

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emem

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all

thre

e fo

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las

list

ed i

n t

he

tabl

e ab

ove.

Wh

ich

of

the

form

s w

ould

you

con

cen

trat

e on

for

wri

tin

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nea

r eq

uat

ion

s? E

xpla

in w

hy

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m.

Sam

ple

an

swer

:P

oin

t-sl

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rm;

the

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pe-

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rcep

t fo

rm

can

be

wri

tten

fro

m t

he

po

int-

slo

pe

form

.Th

is is

so

bec

ause

th

e y-

inte

rcep

t le

ts y

ou

wri

te t

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coo

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ates

of

the

po

int

wh

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line

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e y-

axis

.Yo

u c

an u

se t

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int

as t

he

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en p

oin

t in

th

e p

oin

t-sl

op

e fo

rmu

la.

©G

lenc

oe/M

cGra

w-H

ill31

0G

lenc

oe A

lgeb

ra 1

Co

llin

eari

ty

You

hav

e le

arn

ed h

ow t

o fi

nd

the

slop

e be

twee

n t

wo

poin

ts o

n a

lin

e.D

oes

it m

atte

r w

hic

h t

wo

poin

ts y

ou u

se?

How

doe

s yo

ur

choi

ce o

f po

ints

aff

ect

the

slop

e-in

terc

ept

form

of

the

equ

atio

n o

f th

e li

ne?

1.C

hoo

se t

hre

e di

ffer

ent

pair

s of

poi

nts

fro

m t

he

grap

h a

t th

e ri

ght.

Wri

te t

he

slop

e-in

terc

ept

form

of

the

lin

e u

sin

g ea

ch p

air.

y�

1x�

1

2.H

ow a

re t

he

equ

atio

ns

rela

ted?

Th

ey a

re t

he

sam

e.

3.W

hat

con

clu

sion

can

you

dra

w f

rom

you

r an

swer

s to

Exe

rcis

es 1

an

d 2?

Th

e eq

uat

ion

of

a lin

e is

th

e sa

me

no

mat

ter

wh

ich

tw

o p

oin

ts

you

ch

oo

se.

Wh

en p

oin

ts a

re c

onta

ined

in

th

e sa

me

lin

e,th

ey a

re s

aid

to b

e co

llin

ear.

Eve

n th

ough

poi

nts

may

loo

kli

ke t

hey

form

a s

trai

ght

line

whe

n co

nnec

ted,

it d

oes

not

mea

n t

hat

th

ey a

ctu

ally

do.

By

chec

kin

g pa

irs

of p

oin

ts o

n a

li

ne

you

can

det

erm

ine

wh

eth

er t

he

lin

e re

pres

ents

a l

inea

r re

lati

onsh

ip.

4.C

hoo

se s

ever

al p

airs

of

poin

ts f

rom

th

e gr

aph

at

the

righ

t an

d w

rite

th

e sl

ope-

inte

rcep

t fo

rm o

f th

e li

ne

usi

ng

each

pai

r.

y�

1x�

0;y

�2x

�2;

y�

2x�

1

5.W

hat

con

clu

sion

can

you

dra

w f

rom

you

r eq

uat

ion

s in

E

xerc

ise

4? I

s th

is a

str

aigh

t li

ne?

Th

e p

oin

ts a

re n

ot

colli

nea

r.T

his

is n

ot

a st

raig

ht

line.

x

y O

x

y

O

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-5

5-5



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

Geo

met

ry:P

aral

lel a

nd

Per

pen

dic

ula

r L

ines

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-6

5-6

©G

lenc

oe/M

cGra

w-H

ill31

1G

lenc

oe A

lgeb

ra 1

Lesson 5-6

Para

llel L

ines

Tw

o n

onve

rtic

alli

nes

are

par

alle

lif

th

ey h

ave

the

sam

e sl

ope.

All

ve

rtic

al l

ines

are

par

alle

l.

Wri

te t

he

slop

e-in

terc

ept

form

for

an

eq

uat

ion

of

the

lin

e th

atp

asse

s th

rou

gh (

�1,

6) a

nd

is

par

alle

l to

th

e gr

aph

of

y�

2x�

12.

A l

ine

para

llel

to

y�

2x�

12 h

as t

he

sam

e sl

ope,

2.R

epla

ce m

wit

h 2

an

d (x

1,y 1

) w

ith

(�

1,6)

in

th

e po

int-

slop

e fo

rm.

y�

y 1�

m(x

�x 1

)P

oint

-slo

pe f

orm

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6 �

2(x

�(�

1))

m�

2; (

x 1,

y 1)

�(�

1, 6

)

y�

6 �

2(x

�1)

Sim

plify

.

y�

6 �

2x�

2D

istr

ibut

ive

Pro

pert

y

y�

2x�

8S

lope

-inte

rcep

t fo

rm

Th

eref

ore,

the

equ

atio

n i

s y

�2x

�8.

Wri

te t

he

slop

e-in

terc

ept

form

for

an

eq

uat

ion

of

the

lin

e th

at p

asse

s th

rou

gh t

he

give

n p

oin

t an

d i

s p

aral

lel

to t

he

grap

h o

f ea

ch e

qu

atio

n.

1.2.

3.

y�

x�

4y

��

x�

3y

�x

�7

4.(�

2,2)

,y�

4x�

25.

(6,4

),y

�x

�1

6.(4

,�2)

,y�

�2x

�3

y�

4x�

10y

�x

�2

y�

�2x

�6

7.(�

2,4)

,y�

�3x

�10

8.(�

1,6)

,3x

�y

�12

9.(4

,�6)

,x�

2y�

5

y�

�3x

�2

y�

�3x

�3

y�

�x

�4

10.F

ind

an e

quat

ion

of

the

lin

e th

at h

as a

y-i

nte

rcep

t of

2 t

hat

is

para

llel

to

the

grap

h o

fth

e li

ne

4x�

2y�

8.y

��

2x�

2

11.F

ind

an e

quat

ion

of

the

lin

e th

at h

as a

y-i

nte

rcep

t of

�1

that

is

para

llel

to

the

grap

h o

fth

e li

ne

x�

3y�

6.y

�x

�1

12.F

ind

an e

quat

ion

of

the

lin

e th

at h

as a

y-i

nte

rcep

t of

�4

that

is

para

llel

to

the

grap

h o

fth

e li

ne

y�

6.y

��

4

1 � 3

1 � 2

1 � 3

1 � 3

4 � 31 � 2

( –3,

3)

x

y

O

4x �

3y

� –

12

( –8,

7)

x

y

O

y �

–1 2x

� 4

2

2

( 5, 1

)x

y

O

y �

x �

8

Exam

ple

Exam

ple

Exer

cises

Exer

cises

©G

lenc

oe/M

cGra

w-H

ill31

2G

lenc

oe A

lgeb

ra 1

Perp

end

icu

lar

Lin

esT

wo

lin

es a

re p

erp

end

icu

lar

if t

hei

r sl

opes

are

neg

ativ

ere

cipr

ocal

s of

eac

h o

ther

.Ver

tica

l an

d h

oriz

onta

l li

nes

are

per

pen

dicu

lar.

Wri

te t

he

slop

e-in

terc

ept

form

for

an

eq

uat

ion

th

at p

asse

s th

rou

gh(�

4,2)

an

d i

s p

erp

end

icu

lar

to t

he

grap

h o

f 2x

�3y

�9.

Fin

d th

e sl

ope

of 2

x�

3y�

9.2x

�3y

�9

Orig

inal

equ

atio

n

�3y

��

2x�

9S

ubtr

act

2xfr

om e

ach

side

.

y�

x�

3D

ivid

e ea

ch s

ide

by �

3.

Th

e sl

ope

of y

�x

�3

is

.So,

the

slop

e of

th

e li

ne

pass

ing

thro

ugh

(�

4,2)

th

at i

s 2 � 3

2 � 3

2 � 3Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

Geo

met

ry:P

aral

lel a

nd

Per

pen

dic

ula

r L

ines

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-6

5-6

Exam

ple

Exam

ple

Exer

cises

Exer

cises

perp

endi

cula

r to

th

is l

ine

is t

he

neg

ativ

e re

cipr

ocal

of

,or

�.

Use

th

e po

int-

slop

e fo

rm t

o fi

nd

the

equ

atio

n.

y�

y 1�

m(x

�x 1

)P

oint

-slo

pe f

orm

y�

2 �

�(x

�(�

4))

m�

�;

(x1,

y1)

�(�

4, 2

)

y�

2 �

�(x

�4)

Sim

plify

.

y�

2 �

�x

�6

Dis

trib

utiv

e P

rope

rty

y�

�x

�4

Slo

pe-in

terc

ept

form

Wri

te t

he

slop

e-in

terc

ept

form

for

an

eq

uat

ion

of

the

lin

e th

at p

asse

s th

rou

gh t

he

give

n p

oin

t an

d i

s p

erp

end

icu

lar

to t

he

grap

h o

f ea

ch e

qu

atio

n.

1.(4

,2),

y�

x�

12.

(2,�

3),y

��

x�

43.

(6,4

),y

�7x

�1

y�

�2x

�10

y�

x�

6y

��

x�

4.(�

8,�

7),y

��

x�

85.

(6,�

2),y

��

3x�

66.

(�5,

�1)

,y�

x�

3

y�

x�

1y

�x

�4

y�

�x

�3

7.(�

9,�

5),y

��

3x�

18.

(�1,

3),2

x�

4y�

129.

(6,�

6),3

x�

y�

6

y�

x�

2y

�2x

�5

y�

�x

�4

10.F

ind

an e

quat

ion

of

the

lin

e th

at h

as a

y-i

nte

rcep

t of

�2

and

is p

erpe

ndi

cula

r to

th

egr

aph

of

the

lin

e x

�2y

�5.

y�

�2x

�2

11.F

ind

an e

quat

ion

of

the

lin

e th

at h

as a

y-i

nte

rcep

t of

5 a

nd

is p

erpe

ndi

cula

r to

th

e gr

aph

of t

he

lin

e 4x

�3y

�8.

y�

x�

53 � 4

1 � 31 � 3

2 � 51 � 3

5 � 234 � 71 � 7

3 � 2

2 � 31 � 2

3 � 23 � 23 � 2

3 � 2

3 � 2

3 � 22 � 3



Skil

ls P

ract

ice

Geo

met

ry:P

aral

lel a

nd

Per

pen

dic

ula

r L

ines

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-6

5-6

©G

lenc

oe/M

cGra

w-H

ill31

3G

lenc

oe A

lgeb

ra 1

Lesson 5-6

Wri

te t

he

slop

e-in

terc

ept

form

of

an e

qu

atio

n o

f th

e li

ne

that

pas

ses

thro

ugh

th

egi

ven

poi

nt

and

is

par

alle

l to

th

e gr

aph

of

each

eq

uat

ion

.

1.2.

3.

y�

2x�

1y

��

xy

�x

�3

4.(3

,2),

y�

3x�

45.

(�1,

�2)

,y�

�3x

�5

6.(�

1,1)

,y�

x�

4

y�

3x�

7y

��

3x�

5y

�x

�2

7.(1

,�3)

,y�

�4x

�1

8.(�

4,2)

,y�

x�

39.

(�4,

3),y

�x

�6

y�

�4x

�1

y�

x�

6y

�x

�5

10.(

4,1)

,y�

�x

�7

11.(

�5,

�1)

,2y

�2x

�4

12.(

3,�

1),3

y�

x�

9

y�

�x

�2

y�

x�

4y

�x

�2

Wri

te t

he

slop

e-in

terc

ept

form

of

an e

qu

atio

n o

f th

e li

ne

that

pas

ses

thro

ugh

th

egi

ven

poi

nt

and

is

per

pen

dic

ula

r to

th

e gr

aph

of

each

eq

uat

ion

.

13.(

�3,

�2)

,y�

x�

214

.(4,

�1)

,y�

2x�

415

.(�

1,�

6),x

�3y

�6

y�

�x

�5

y�

�x

�1

y�

3x�

3

16.(

�4,

5),y

��

4x�

117

.(�

2,3)

,y�

x�

418

.(0,

0),y

�x

�1

y�

x�

6y

��

4x�

5y

��

2x

19.(

3,�

3),y

�x

�5

20.(

�5,

1),y

��

x�

721

.(0,

�2)

,y�

�7x

�3

y�

�x

�1

y�

x�

4y

�x

�2

22.(

2,3)

,2x

�10

y�

323

.(�

2,2)

,6x

�3y

��

924

.(�

4,�

3),8

x�

2y�

16

y�

5x�

7y

�x

�3

y�

�x

�4

1 � 41 � 2

1 � 73 � 5

4 � 3

5 � 33 � 4

1 � 4

1 � 21 � 4

1 � 2

1 � 31 � 4

1 � 4

1 � 2

1 � 2

1 � 2

( –2,

2)

x

y O

y �

1 2x �

1( 1

, –1)

x

y

O

y �

–x

� 3

( –2,

–3)

x

y O

y �

2x

� 1

©G

lenc

oe/M

cGra

w-H

ill31

4G

lenc

oe A

lgeb

ra 1

Wri

te t

he

slop

e-in

terc

ept

form

of

an e

qu

atio

n o

f th

e li

ne

that

pas

ses

thro

ugh

th

egi

ven

poi

nt

and

is

par

alle

l to

th

e gr

aph

of

each

eq

uat

ion

.

1.(3

,2),

y�

x�

52.

(�2,

5),y

��

4x�

23.

(4,�

6),y

��

x�

1

y�

x�

1y

��

4x�

3y

��

x�

3

4.(5

,4),

y�

x�

25.

(12,

3),y

�x

�5

6.(3

,1),

2x�

y�

5

y�

x�

2y

�x

�13

y�

�2x

�7

7.(�

3,4)

,3y

�2x

�3

8.(�

1,�

2),3

x�

y�

59.

(�8,

2),5

x�

4y�

1

y�

x�

6y

�3x

�1

y�

x�

12

10.(

�1,

�4)

,9x

�3y

�8

11.(

�5,

6),4

x�

3y�

112

.(3,

1),2

x�

5y�

7

y�

�3x

�7

y�

�x

�y

��

x�

Wri

te t

he

slop

e-in

terc

ept

form

of

an e

qu

atio

n o

f th

e li

ne

that

pas

ses

thro

ugh

th

egi

ven

poi

nt

and

is

per

pen

dic

ula

r to

th

e gr

aph

of

each

eq

uat

ion

.

13.(

�2,

�2)

,y�

�x

�9

14.(

�6,

5),x

�y

�5

15.(

�4,

�3)

,4x

�y

�7

y�

3x�

4y

��

x�

1y

�x

�2

16.(

0,1)

,x�

5y�

1517

.(2,

4),x

�6y

�2

18.(

�1,

�7)

,3x

�12

y�

�6

y�

5x�

1y

��

6x�

16y

�4x

�3

19.(

�4,

1),4

x�

7y�

620

.(10

,5),

5x�

4y�

821

.(4,

�5)

,2x

�5y

��

10

y�

x�

8y

�x

�3

y�

�x

�5

22.(

1,1)

,3x

�2y

��

723

.(�

6,�

5),4

x�

3y�

�6

24.(

�3,

5),5

x�

6y�

9

y�

x�

y�

x�

y�

�x

�

25.G

EOM

ETRY

Qu

adri

late

ral

AB

CD

has

dia

gon

als

A�C�

and

B�D�

.D

eter

min

e w

het

her

A �C�

is p

erpe

ndi

cula

r to

B�D�

.Exp

lain

.

Yes;

they

are

per

pen

dic

ula

r b

ecau

se t

hei

r sl

op

es a

re

7 an

d �

,wh

ich

are

neg

ativ

e re

cip

roca

ls.

26.G

EOM

ETRY

Tri

angl

e A

BC

has

ver

tice

s A

(0,4

),B

(1,2

),an

d C

(4,6

).D

eter

min

e w

het

her

tri

angl

e A

BC

is a

rig

ht

tria

ngl

e.E

xpla

in.

Yes;

sid

es A�

B�an

d A�

C�ar

e p

erp

end

icu

lar

bec

ause

th

eir

slo

pes

are

�2

and

,w

hic

h a

re n

egat

ive

reci

pro

cals

.1 � 2

1 � 7

x

y O

A

D

C

B

7 � 56 � 5

1 � 23 � 4

1 � 32 � 3

5 � 24 � 5

7 � 4

1 � 4

1 � 3

11 � 52 � 5

2 � 34 � 3

5 � 42 � 3

4 � 32 � 5

4 � 32 � 5

3 � 4

3 � 4

Pra

ctic

e (

Ave

rag

e)

Geo

met

ry:P

aral

lel a

nd

Per

pen

dic

ula

r L

ines

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-6

5-6



An

swer

s

Readin

g t

o L

earn

Math

em

ati

csG

eom

etry

:P

aral

lel a

nd

Per

pen

dic

ula

r L

ines

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-6

5-6

©G

lenc

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ill31

5G

lenc

oe A

lgeb

ra 1

Lesson 5-6

Pre-

Act

ivit

yH

ow c

an y

ou d

eter

min

e w

het

her

tw

o li

nes

are

par

alle

l?

Rea

d th

e in

trod

uct

ion

to

Les

son

5-6

at

the

top

of p

age

292

in y

our

text

book

.

•W

hat

is

a fa

mil

y of

gra

phs?

A g

rou

p o

f g

rap

hs

that

hav

e at

leas

to

ne

char

acte

rist

ic in

co

mm

on

,su

ch a

s sl

op

e o

r y-

inte

rcep

t.

•D

o yo

u t

hin

k li

nes

th

at d

o n

ot a

ppea

r to

in

ters

ect

are

para

llel

or

perp

endi

cula

r?p

aral

lel

Rea

din

g t

he

Less

on

1.R

efer

to

the

Key

Con

cept

box

on

pag

e 29

2.W

hy

does

th

e de

fin

itio

n u

se t

he

term

non

vert

ical

wh

en t

alki

ng

abou

t li

nes

wit

h t

he

sam

e sl

ope?

Ver

tica

l lin

es h

ave

slo

pes

th

at a

re u

nd

efin

ed s

o w

e ca

nn

ot

say

they

hav

e th

e sa

me

slo

pe.

2.W

hat

is

a ri

ght

angl

e?S

amp

le a

nsw

ers:

A r

igh

t an

gle

is o

ne

that

mea

sure

s90

°.It

is a

n a

ng

le f

orm

ed b

y p

erp

end

icu

lar

lines

.

3.R

efer

to

the

Key

Con

cept

box

on

pag

e 29

3.D

escr

ibe

how

you

fin

d th

e op

posi

te r

ecip

roca

lof

a n

um

ber.

Sam

ple

an

swer

:Th

e re

cip

roca

l of

a g

iven

nu

mb

er is

th

en

um

ber

fo

rmed

wh

en y

ou

sw

itch

th

e n

um

erat

or

and

den

om

inat

or.

Th

enyo

u g

ive

it t

he

op

po

site

sig

n o

f th

e o

rig

inal

nu

mb

er.

4.W

rite

th

e op

posi

te r

ecip

roca

l of

eac

h n

um

ber.

a.2

�b

.�

3c.

�d

.�

5

Hel

pin

g Y

ou

Rem

emb

er

5.O

ne

way

to

rem

embe

r h

ow s

lope

s of

par

alle

l li

nes

are

rel

ated

is

to s

ay “

sam

e di

rect

ion

,sa

me

slop

e.”

Try

to

thin

k of

a p

hra

se t

o h

elp

you

rem

embe

r th

at p

erpe

ndi

cula

r li

nes

hav

e sl

opes

th

at a

re o

ppos

ite

reci

proc

als.

Sam

ple

an

swer

:N

icel

y ri

gh

t an

gle

s fo

rmed

,use

op

po

site

rec

ipro

cals

.

1 � 513 � 12

12 � 131 � 3

1 � 2

©G

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6G

lenc

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lgeb

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Pen

cils

of

Lin

esA

ll o

f th

e li

nes

th

at p

ass

thro

ugh

a

sin

gle

poin

t in

th

e sa

me

plan

e ar

e ca

lled

a p

enci

l of

lin

es.

All

lin

es w

ith

th

e sa

me

slop

e,bu

t di

ffer

ent

inte

rcep

ts,a

re a

lso

call

ed a

“pe

nci

l,”a

pen

cil o

f p

aral

lel l

ines

.

Gra

ph

som

e of

th

e li

nes

in

eac

h p

enci

l.

1.A

pen

cil

of l

ines

th

rou

gh t

he

2.A

pen

cil

of l

ines

des

crib

ed b

y po

int

(1,3

)y

�4

�m

(x�

2),w

her

e m

is a

ny

real

nu

mbe

r

3.A

pen

cil

of l

ines

par

alle

l to

th

e li

ne

4.A

pen

cil

of l

ines

des

crib

ed b

y x

�2y

�7

y�

mx

�3m

�2

x

y

Ox

y

O

x

y

Ox

y

O

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-6

5-6



Stu

dy G

uid

e a

nd I

nte

rven

tion

Sca

tter

Plo

ts a

nd

Lin

es o

f F

it

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-7

5-7

©G

lenc

oe/M

cGra

w-H

ill31

7G

lenc

oe A

lgeb

ra 1

Lesson 5-7

Inte

rpre

t Po

ints

on

a S

catt

er P

lot

A s

catt

er p

lot

is a

gra

ph i

n w

hic

h t

wo

sets

of

data

are

plo

tted

as

orde

red

pair

s in

a c

oord

inat

e pl

ane.

If y

incr

ease

s as

xin

crea

ses,

ther

e is

a p

osit

ive

corr

elat

ion

betw

een

xan

d y.

If y

decr

ease

s as

xin

crea

ses,

ther

e is

a n

egat

ive

corr

elat

ion

betw

een

xan

d y.

If x

and

yar

e n

ot r

elat

ed,t

her

e is

no

corr

elat

ion

.

EAR

NIN

GS

Th

e gr

aph

at

the

righ

t sh

ows

the

amou

nt

of m

oney

Car

men

ear

ned

eac

hw

eek

an

d t

he

amou

nt

she

dep

osit

ed i

n h

er s

avin

gsac

cou

nt

that

sam

e w

eek

.Det

erm

ine

wh

eth

er t

he

grap

h s

how

s a

pos

itiv

e co

rrel

atio

n,a

neg

ativ

eco

rrel

atio

n,o

r n

o co

rrel

atio

n.I

f th

ere

is a

p

osit

ive

or n

egat

ive

corr

elat

ion

,des

crib

e it

sm

ean

ing

in t

he

situ

atio

n.

The

gra

ph s

how

s a

posi

tive

cor

rela

tion

.The

mor

e C

arm

en e

arns

,the

mor

e sh

e sa

ves.

Det

erm

ine

wh

eth

er e

ach

gra

ph

sh

ows

a p

osit

ive

corr

elat

ion

,a n

egat

ive

corr

elat

ion

,or

no

corr

elat

ion

.If

ther

e is

a p

osit

ive

corr

elat

ion

,des

crib

e it

.

1.2.

no

co

rrel

atio

nN

egat

ive

corr

elat

ion

;as

tim

e

incr

ease

s,sp

eed

dec

reas

es.

3.4.

Po

siti

ve c

orr

elat

ion

;as

th

e P

osi

tive

co

rrel

atio

n;

as t

he

nu

mb

er o

f ye

ars

incr

ease

s,th

e n

um

ber

of

year

s in

crea

ses,

the

nu

mb

er o

f cl

ub

s in

crea

ses.

nu

mb

er o

f fu

nd

s in

crea

ses.

Nu

mb

er

of

Mu

tual

Fun

ds

Year

s Si

nce

199

1

Number of Funds(thousands)

02

41

35

67

7 6 5 4 3

Sour

ce: T

he W

all S

treet

Jour

nal A

lman

ac

Gro

wth

of

Invest

men

t C

lub

s

Year

s Si

nce

199

0

Number of Clubs(thousands)

02

41

35

67

8

35 28 21 14 7

Sour

ce: T

he W

all S

treet

Jour

nal A

lman

ac

Avera

ge J

og

gin

g S

peed

Min

ute

s

Miles per Hour

010

205

1525

10 5

Avera

ge W

eekly

Wo

rk H

ou

rs i

n U

.S.

Year

s Si

nce

199

0

Hours

02

46

17

89

x

y

35

34.8

34.6

34.4

34.2

Sour

ce: T

he W

orld

Alm

anac

Carm

en

’s E

arn

ing

s an

d S

avin

gs

Do

llars

Ear

ned

Dollars Saved

040

8012

0

35 30 25 20 15 10 5

Exam

ple

Exam

ple

Exer

cises

Exer

cises

©G

lenc

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ill31

8G

lenc

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lgeb

ra 1

Lin

es o

f Fi

t

Th

e ta

ble

bel

ow s

how

s th

e n

um

ber

of

stu

den

ts p

er c

omp

ute

r in

Un

ited

Sta

tes

pu

bli

c sc

hoo

ls f

or c

erta

in s

choo

l ye

ars

from

199

0 to

200

0.

Year

1990

1992

1994

1996

1998

2000

Stu

den

ts p

er C

om

pu

ter

2218

1410

6.1

5.4

a.D

raw

a s

catt

er p

lot

and

det

erm

ine

wh

at

rela

tion

ship

exi

sts,

if a

ny.

Sin

ce y

decr

ease

s as

xin

crea

ses,

the

corr

elat

ion

is

neg

ativ

e.

b.

Dra

w a

lin

e of

fit

for

th

e sc

atte

r p

lot.

Dra

w a

lin

e th

at p

asse

s cl

ose

to m

ost

of t

he

poin

ts.A

lin

e of

fit

is

show

n.

c.W

rite

th

e sl

ope-

inte

rcep

t fo

rm o

f an

equ

atio

n f

or t

he

lin

e of

fit

.T

he

lin

e of

fit

sh

own

pas

ses

thro

ugh

(1

993,

16)

and

(199

9,5.

7).F

ind

the

slop

e.

m�

m�

�1.

7

Fin

d b

in y

��

1.7x

�b.

16 �

�1.

7 �

1993

�b

3404

�b

Th

eref

ore,

an e

quat

ion

of

a li

ne

of f

it i

s y

��

1.7x

�34

04.

Ref

er t

o th

e ta

ble

for

Exe

rcis

es 1

–3.

1.D

raw

a s

catt

er p

lot.

3.W

rite

th

e sl

ope-

inte

rcep

t

2.D

raw

a l

ine

of f

it f

or t

he

data

.fo

rm o

f an

equ

atio

n f

or t

he

lin

e of

fit

.

Th

e p

oin

ts (

0,11

.43)

and

(2,

12.2

8) g

ive

y�

0.42

5x�

11.4

3 as

a

line

of

fit.

U.S

. Pro

du

ctio

nW

ork

ers

Ho

url

y W

ag

e

Year

s Si

nce

199

5

Hourly Wage (dollars)

01

32

45

67

14 13 12 11

Sour

ce: T

he W

orld

Alm

anac

Year

sH

ou

rly

Sin

ce 1

995

Wag

e

0$1

1.43

1$1

1.82

2$1

2.28

3$1

2.78

4$1

3.24

5.7

�16

��

1999

�19

93

Stu

den

ts p

er

Co

mp

ute

rin

U.S

. Pu

bli

c Sch

oo

ls

Year

Students per Computer

1990

1992

1994

1996

1998

2000

24 20 16 12 8 4 0

Sour

ce: T

he W

orld

Alm

anac

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

Sca

tter

Plo

ts a

nd

Lin

es o

f F

it

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-7

5-7

Exam

ple

Exam

ple

Exer

cises

Exer

cises



An

swer

s

Skil

ls P

ract

ice

Sta

tist

ics:

Sca

tter

Plo

ts a

nd

Lin

es o

f F

it

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

5-7

5-7

©G

lenc

oe/M

cGra

w-H

ill31

9G

lenc

oe A

lgeb

ra 1

Lesson 5-7

Det

erm

ine

wh

eth

er e

ach

gra

ph

sh

ows

a p

osit

ive

corr

ela

tion

,a n

ega

tive

corr

ela

tion

,or

no

corr

ela

tion

.If

ther

e is

a p

osit

ive

or n

egat

ive

corr

elat

ion

,d

escr

ibe

its

mea

nin

g in

th

e si

tuat

ion

.

1.2.

Po

siti

ve;

the

lon

ger

th

e ex

erci

se,

no

co

rrel

atio

nth

e m

ore

Cal

ori

es b

urn

ed.

3.4.

Neg

ativ

e;as

wei

gh

t in

crea

ses,

Neg

ativ

e;as

th

e ye

ar in

crea

ses,

the

nu

mb

er o

f re

pet

itio

ns

the

nu

mb

er o

f ev

enin

g

dec

reas

es.

new

spap

ers

dec

reas

es.

BA

SEB

ALL

For

Exe

rcis

es 5

–7,u

se t

he

scat

ter

plo

t th

at s

how

s th

e av

erag

e p

rice

of

a m

ajor

-lea

gue

bas

ebal

l ti

cket

fro

m 1

991

to 2

000.

5.D

eter

min

e w

hat

rel

atio

nsh

ip,i

f an

y,ex

ists

in

th

e da

ta.E

xpla

in.

Po

siti

ve c

orr

elat

ion

;as

the

year

incr

ease

s,th

e p

rice

incr

ease

s.6.

Use

th

e po

ints

(19

93,9

.60)

an

d (1

998,

13.6

0)

to w

rite

th

e sl

ope-

inte

rcep

t fo

rm o

f an

equ

atio

nfo

r th

e li

ne

of f

it s

how

n i

n t

he

scat

ter

plot

.y

�0.

8x�

1584

.87.

Pre

dict

th

e pr

ice

of a

tic

ket

in 2

004.

abo

ut

$18.

40

Base

ball

Tic

ket

Pri

ces

Year

Average Price ($)

’91

’92

’93

’94

’95

’96

’97

’98

’99

18 16 14 12 10 8 0’0

0

Sour

ce: T

eam

Mar

ketin

g Re

port,

Chi

cago

Even

ing

New

spap

ers

Year

Number of Newspapers

’91

’92

’93

’94

’95

’96

’97

’98

’99

1050

1000 950

900

850

800

750 0

Sour

ce: E

dito

r & P

ublis

her

Weig

ht-

Lift

ing

Wei

gh

t (p

ou

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s)

Repetitions

040

8020

6010

012

014

0

14 12 10 8 6 4 2

Lib

rary

Fin

es

Bo

oks

Bo

rro

wed

Fines (dollars)

02

45

67

88

13

10

7 6 5 4 3 2 1

Calo

ries

Bu

rned

Du

rin

g E

xerc

ise

Tim

e (m

inu

tes)

Calories

020

4010

3050

60

600

500

400

300

200

100

©G

lenc

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ill32

0G

lenc

oe A

lgeb

ra 1

Det

erm

ine

wh

eth

er e

ach

gra

ph

sh

ows

a p

osit

ive

corr

ela

tion

,a n

ega

tive

corr

ela

tion

,or

no

corr

ela

tion

.If

ther

e is

a p

osit

ive

or n

egat

ive

corr

elat

ion

,d

escr

ibe

its

mea

nin

g in

th

e si

tuat

ion

.

1.2.

no

co

rrel

atio

nP

osi

tive

;as

the

mea

n e

leva

tio

nin

crea

ses,

the

hig

hes

t p

oin

t in

crea

ses.

DIS

EASE

For

Exe

rcis

es 3

–6,u

se t

he

tab

le t

hat

sh

ows

the

nu

mb

er o

f ca

ses

of m

um

ps

in t

he

Un

ited

Sta

tes

for

the

year

s 19

95 t

o 19

99.

3.D

raw

a s

catt

er p

lot

and

dete

rmin

e w

hat

re

lati

onsh

ip,i

f an

y,ex

ists

in

th

e da

ta.

Sour

ce:C

ente

rs fo

r Dise

ase

Cont

rol a

nd P

reve

ntio

n

Neg

ativ

e co

rrel

atio

n;

as t

he

year

in

crea

ses,

the

nu

mb

er o

f ca

ses

dec

reas

es.

4.D

raw

a l

ine

of f

it f

or t

he

scat

ter

plot

.S

amp

le a

nsw

er:

Use

(19

96,7

51),

(199

7,68

3).

5.W

rite

th

e sl

ope-

inte

rcep

t fo

rm o

f an

equ

atio

n f

or t

he

line

of

fit.

Sam

ple

an

swer

:y�

�68

x�

136,

479

6.P

redi

ct t

he

nu

mbe

r of

cas

es i

n 2

004.

abo

ut

207

ZOO

SF

or E

xerc

ises

7–1

0,u

se t

he

tab

le t

hat

sh

ows

the

aver

age

and

max

imu

m l

onge

vity

of

vari

ous

anim

als

in c

apti

vity

.

7.D

raw

a s

catt

er p

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5-7

5-7



Readin

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earn

Math

em

ati

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tati

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s:S

catt

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lots

an

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5-7

5-7

©G

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1G

lenc

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lgeb

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Lesson 5-7

Pre-

Act

ivit

yH

ow d

o sc

atte

r p

lots

hel

p i

den

tify

tre

nd

s in

dat

a?

Rea

d th

e in

trod

uct

ion

to

Les

son

5-7

at

the

top

of p

age

298

in y

our

text

book

.

•W

hat

doe

s th

e ph

rase

lin

ear

rela

tion

ship

mea

n t

o yo

u?

Sam

ple

answ

er:

It m

ean

s th

at w

hen

yo

u g

rap

h t

he

dat

a p

oin

ts o

n a

coo

rdin

ate

gri

d,t

he

po

ints

all

lie o

n o

r cl

ose

to

a li

ne

that

you

co

uld

dra

w o

n t

he

gri

d.

•W

rite

th

ree

orde

red

pair

s th

at f

it t

he

desc

ript

ion

as

x in

crea

ses,

yd

ecre

ases

.S

amp

le a

nsw

er:

{(2,

5),(

3,3)

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1)}

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din

g t

he

Less

on

1.L

ook

up

the

wor

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atte

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ow d

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this

def

init

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com

pare

to

the

term

scat

ter

plot

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ne

def

init

ion

sta

tes

“to

occ

ur

or

fall

irre

gu

larl

y o

r at

ran

do

m.”

Th

e p

oin

ts in

a s

catt

er p

lots

usu

ally

do

no

t fo

llow

an

exa

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ear

pat

tern

,bu

t fa

ll ir

reg

ula

rly

on

th

e co

ord

inat

e p

lan

e.

2.W

hat

is

a li

ne

of f

it?

How

man

y da

ta p

oin

ts f

all

on t

he

lin

e of

fit

?A

lin

e o

f fi

t sh

ow

sth

e tr

end

of

the

dat

a.It

is im

po

ssib

le t

o s

ay h

ow

man

y d

ata

po

ints

may

fall

on

a li

ne

of

fit—

may

be

seve

ral,

may

be

no

ne.

3.W

hat

is

lin

ear

inte

rpol

atio

n?

How

can

you

dis

tin

guis

h i

t fr

om l

inea

r ex

trap

olat

ion

?L

inea

r in

terp

ola

tio

n is

th

e p

roce

ss o

f p

red

icti

ng

a y

-val

ue

for

a g

iven

x-

valu

e th

at li

es b

etw

een

th

e le

ast

and

gre

ates

t x-

valu

es in

th

e d

ata

set.

“In

ter-

”m

ean

s b

etw

een

an

d “

extr

a-”

mea

ns

bey

on

d.I

f th

e x-

valu

e is

bet

wee

n t

he

extr

emes

of

the

x-va

lues

in t

he

dat

a se

t,yo

u s

ayin

terp

ola

tio

n;

if t

he

x-va

lue

is le

ss t

han

or

gre

ater

th

an t

he

extr

emes

,yo

u s

ay e

xtra

po

lati

on

.

Hel

pin

g Y

ou

Rem

emb

er

4.H

ow c

an y

ou r

emem

ber

wh

eth

er a

set

of

data

poi

nts

sh

ows

a po

siti

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orre

lati

on o

r a

neg

ativ

e co

rrel

atio

n?

If it

loo

ks li

ke a

lin

e o

f fi

t fo

r th

e p

oin

ts w

ou

ld h

ave

ap

osi

tive

slo

pe,

ther

e is

a p

osi

tive

co

rrel

atio

n.I

f it

loo

ks li

ke a

lin

e o

f fi

tw

ou

ld h

ave

a n

egat

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slo

pe,

ther

e is

a n

egat

ive

corr

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.

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Lat

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re

Th

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titu

de

of a

pla

ce o

n E

arth

is t

he

mea

sure

of

its

dist

ance

from

th

e eq

uat

or.W

hat

do

you

thin

k is

th

e re

lati

onsh

ip

betw

een

a c

ity’

s la

titu

de a

nd

its

Jan

uar

y te

mpe

ratu

re?

At

the

righ

t is

a t

able

con

tain

ing

the

lati

tude

s an

d Ja

nu

ary

mea

n t

empe

ratu

res

for

fift

een

U.S

.cit

ies.

Sam

ple

an

swer

s ar

e g

iven

.

Sour

ces:

www.

indo

.com

and

www

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a.gov

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atex

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l

1.U

se t

he

info

rmat

ion

in

th

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to c

reat

e

a sc

atte

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ot a

nd

draw

a l

ine

of b

est

fit

for

the

data

.

2.W

rite

an

equ

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lin

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fit

.Mak

e a

con

ject

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abo

ut

the

rela

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cit

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y�

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se y

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o pr

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t th

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as y

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the

rela

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as t

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tem

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ME

____

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____

____

____

____

____

____

____

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____

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AT

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____

____

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ER

IOD

____

_

5-7

5-7



1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. D

C

D

B

C

A

D

B

B

A

A

7

D

D

A

B

A

B

B

B

C

C

C

A

D

C

B

D

D

A

C

B

An

swer

s

(continued on the next page)

Chapter 5 Assessment Answer Key Form 1 Form 2APage 323 Page 324 Page 325


12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: �21

C

B

A

C

D

A

B

A

B

C

A

B

B

D

B

B

B

A

C

D

�137�

C

B

A

C

D

B

C

B

C

Chapter 5 Assessment Answer Key Form 2A (continued) Form 2BPage 326 Page 327 Page 328


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: � � 1.2t � 1.8; 6 years

Sample answer: Using data points (20, 67) and(40, 87), y � x � 47; 82

Time Spent Studying(minutes)

Sco

re R

ecei

ved

(per

cen

t)

0

60

70

80

90

100

10 20 30 40 50

y � �23

�x � 4

y � �2x � 1

y � 3x � 10

12x � 7y � �16

y � 8 � �13

�(x � 2)

x � �6

y � �32

�x � �12

�

y

xO

y � �23

�x � 2

5x � 7y � 14

y � 0.10x � 28.75

d � 3t; 36 mi

y

xO

about �0.49

�25

��191�

0

1

An

swer

s

Chapter 5 Assessment Answer Key Form 2CPage 329 Page 330


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:y � �

65

�x � 6

Sample answer:Using data points (30, 6.1) and(70, 4.7), y � �0.035x � 7.15;about 4.9

Age

Perc

ent

Spen

t o

nEn

tert

ain

men

t

3

4

5

6

30 40 50 60 70 80

y � ��14

�x � 4

y � �3x � 18

y � �34

�x � �54

�

2x � 3y � �1

y � �43

�(x � 3)

x � 5

y � �5x � 29

y

xO

y � ��23

�x � 2

x � y � 2

y � 2.50x � 4.95

�12

�h

y

xO

about ��13

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1

undefined

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0

Chapter 5 Assessment Answer Key Form 2DPage 331 Page 332


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B: 9

y � �0.5x � 2

Sample answer:y � 52.99 � 0.12(x � 200)

Sample answer:Using data points

(424, 466) and (460, 488) y � 0.6x � 211.6; about 479

Positive; a verbal scoreis closely associatedwith the math score

Verbal Score

Mat

h S

core

450

460

470

480

490

500

400420440460480

y � 5

y � �35

�x � 6

y � ��43

�x � 9

x � 3

y � 6

y � ��35

�x � �256�

y � �52

�x � 11

y � 3x � 8

y � 2 � ��23�x

2x � 3y � 6

y

xO

2x � y � 1

y � 1� ��35

�(x � 2)

60

y

xO

about 690 people/yr

�7103�

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An

swer

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nsw

ers

Chapter 5 Assessment Answer Key Form 3Page 333 Page 334


Chapter 5 Assessment Answer KeyPage 335, Open-Ended Assessment

Scoring Rubric

Score General Description Specific Criteria

• Shows thorough understanding of the concepts of slope,various forms of a linear equation, graphing lines from anequation, scatter plots, correlation, and predicting data.

• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.

• Shows an understanding of the concepts of slope, variousforms of a linear equation, graphing lines from anequation, scatter plots, correlation, and predicting data.

• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.

• Shows an understanding of most of the concepts of slope,various forms of a linear equation, graphing lines from anequation, scatter plots, correlation, and predicting data.

• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs are mostly accurate.• Satisfies the requirements of most of the problems.

• Final computation is correct.• No written explanations or work is shown to substantiate

the final computation.• Graphs may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.

• Shows little or no understanding of most of the concepts ofslope, various forms of a linear equation, graphing linesfrom an equation, scatter plots, correlation, and predictingdata.

• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs are inaccurate or inappropriate.• Does not satisfy the requirements of problems.• No answer may be given.

0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given

1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation

2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem

3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation

4 SuperiorA correct solution that is supported by well-developed, accurateexplanations


1a. After drawing a graph, students shouldexplain that they can use the two pointson the graph to determine the slope.This can be done by counting squaresfor the rise and run of the line or byusing the coordinates of the points inthe slope formula.

1b. The slope is the value of m in the slope-intercept form y � mx � b. Bysubstituting the value of m and thecoordinates of one of the points for x andy, the value of b can be found and anequation written using m and b. Theslope and either ordered pair can beused to write the point-slope form of anequation. The standard form of anequation is an algebraic manipulation ofeither of the other two forms ofequations. See students’ equations forthe line drawn.

2a. In order to graph the line through (�2, 3) you need to know the slope ofthe line, another point on the line, orthe equation of the line.

2b. If you knew the slope of the line, youcould plot another point using the riseand run on a coordinate plane. If youknew another point, you could graphthat point and draw a line through (�2, 3) and the other point. If you knewthe equation of the line, you could usethe slope-intercept form of the equationto find the slope and intercept forgraphing or you could use the equationand substitution to find another pointon the line.

3a. The points have a strong negativecorrelation. This means that as xincreases, y decreases.

3b. One example is the longer a candleburns, the shorter it gets. Another is thelonger you run a car, the less gasoline isleft in the tank.

3c. See students’ work.

4a.

4b. While students’ knowledge from otherexperiences may lead them to thatconclusion, there may be other factorsthat contribute to increased longevity.The information on the graph only leadsus to claim that life expectancy isincreasing.

4c. A regression equation calculated by agraphing calculator would yield aprediction of 78.9 years. However,students may look at the era since 1980and notice that each 5-year period isabout 0.3 year less than the previous 5-year period increase. This patternwould yield a prediction of about 75.9years.

50

55

60

65

70

75

80

'20'30'40'50'60'70'80 '90 '00Year of Birth

Life

Exp

ecta

ncy

(yea

rs)

An

swer

s

Chapter 5 Assessment Answer Key Page 335, Open-Ended Assessment

Sample Answers

In addition to the scoring rubric found on page A28, the following sample answers may be used as guidance in evaluating open-ended assessment items.


1. perpendicular lines;parallel lines

2. constant ofvariation

3. scatter plot

4. family of graphs

5. rate of change

6. linear interpolation

7. slope

8. slope-intercept

9. point-slope

10. standard

11. Sample answer:A line of fit is a linethat comes close tothe data points for ascatter plot, even ifall the data pointsdo not lie on thatline.

12. Sample answer:Linear extrapolationis the process ofusing a linearequation to predicta y value for an x value that liesbeyond theextremes of thedomain of therelation.

1.

2.

3.

4.

5.

Quiz (Lessons 5–3 and 5–4)

Page 337

1.

2.

3.

4.

5.

1.

2.

3.

4.

5.

Quiz (Lesson 5–7)

Page 338

1–2.

3.

4.

5. Sample answer: $35,850

Sample answer: Usingdata points (27, 19.1)

and (29, 25.8),y � 3.35x � 71.35

Positive; the older youget, the greater your

income.

Age

Med

ian

Inco

me

($10

00)

16

19

22

25

28

31

26 27 28 29 30

y � ��49

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y � ��13

�x � �134�

y � 1 � 0

y � �x � 7

y � 6 � ��13

�(x � 3)

C

h � 3y � 48 for h ininches or h � 0.25y � 4

for h in feet

y

xO

y � ��141�x � �

5181�

y � �14

�x � 5

$285

5 students/yr

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Chapter 5 Assessment Answer Key Vocabulary Test/Review Quiz (Lessons 5–1 and 5–2) Quiz (Lessons 5–5 and 5–6)

Page 336 Page 337 Page 338


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.y � �

53

�x � 4

x � �6

y � �3x � 12

�57

�

y � �32

�x � 2

Yes, exactly one memberof the range is paired

with each member of thedomain.

{�7.5, �6.5, �6,�5, �3.5}

�7

�89

�

�8

�2a � 3b

�30y

�15.1

�112�

�4438�

2�14

�

0

2r2s2

y � �13

�x � �23

�

�13

�

y � �3x � 2

y � x � 2

y � ��34

�x � 5

A

B

A

A

C

An

swer

s

Chapter 5 Assessment Answer Key Mid-Chapter Test Cumulative ReviewPage 339 Page 340


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. 12.

13. 14.

15.

16. DCBA

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Chapter 5 Assessment Answer KeyStandardized Test Practice

Page 341 Page 342

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Chapter 5 Resource Masters - Math Problem Solvingjaeproblemsolving.weebly.com/uploads/5/1/9/6/51966985/...©Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using the