Problem Set - Chamblee Middle Schoolchambleems.dekalb.k12.ga.us/Downloads/Student Skills Practice Ch… · Luis is shoveling snow from driveways in his neighborhood to save money

Chapter 12 Skills Practice • 737

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Lesson 12.1 Skills Practice

Name ________________________________________________________ Date _________________________

Willie CatchemAnalyzing Problem Situations Using Multiple Representations

Problem SetWrite an equation that represents the relationship shown in each table. Use the equation

to answer the question.

1. Terell is biking around a track. The table show the time it takes Terell to complete several laps

around the track. Write an equation that represents the relationship shown in the table. If Terell

bikes around the track for 1 hour, how many laps will he complete?

Time (minutes) Distance (laps)

0 0

12 9

24 18

Let t 5 time (minutes)

Let d 5 distance (laps)

speed 5 9 laps ___________

12 minutes

5 0.75 lap per minute

d 5 0.75t

1 hour 5 60 minutes

d 5 0.75t

5 0.75(60)

5 45

If Terell bikes around the track for 1 hour, he will complete 45 laps.

738 • Chapter 12 Skills Practice

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Lesson 12.1 Skills Practice page 2

2. Claudia is jogging around her neighborhood. The table shows the distance Claudia travels during

her jog. Write an equation that represents the relationship shown in the table. How long will it take

Claudia to jog 5 miles?

Time (hours) Distance (miles)

0 0

0.5 1.5

0.75 2.25


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Name ________________________________________________________ Date _________________________

3. Shawna is driving to the beach for summer vacation. The table shows the distance Shawna travels

during her trip. Write an equation that represents the relationship shown in the table. How long will

it take Claudia to drive the entire 500 mile trip?


0 0

2 110

3 165


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4. Mattie and Lavonne agree to meet and make signs for the pep rally. Lavonne starts 30 minutes

early and completes 2 signs before Mattie arrives. The table shows the total number of signs the

girls have completed at different times after Mattie arrives. Write an equation that represents the

relationship shown in the table. If the girls work for 3 hours after Mattie arrives, what is the total

number of signs the girls will complete?

Time (hours) Number of Signs

20.5 0

0 2

0.5 4


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Name ________________________________________________________ Date _________________________

5. Juan leaves his home and rides his bike for 15 minutes to the park. After he gets to the park, he

resets his odometer to 0 and continues to ride at the same speed. The table shows the distance

Juan traveled at the park according to his odometer. Write an equation that represents the

relationship shown in the table. If it has been 1.5 hours since Juan left home, what is the distance

he rode his bike at the park?


0.25 0

0.5 1.25

0.75 2.5


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6. Lee is a member of the drama club. He is setting up chairs in the gym for the school play. He

arrives 5 minutes early and sets up 25 chairs before Jin arrives to help. The table shows the total

number of chairs set up at different times after Jin arrives. Write an equation that represents the

relationship shown in the table. If Lee and Jin continue at the same pace, how long will it take to

set up 300 chairs?

Time (minutes) Number of Chairs

25 0

0 25

10 75


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Name ________________________________________________________ Date _________________________

Complete each table using the given equation. Use the table to graph the equation.

7. Joelle is ice skating around an ice rink. The equation d 5 0.5t represents the relationship between

the time Joelle skates in minutes, t, and the distance she skates in laps, d. Complete the table.

Graph the points on the grid.

Time (minutes) Distance (laps)

0 0

10 5

20 10

30 15

-30

-40

-30-40-50

Dis

tanc

e (la

ps)

-20 -10

Time (minutes)

0 10 20 30 40 50

x

y

-10

0

10

20

30

40

-50

-20

50


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8. Leon is jogging around a park. The equation d 5 5t represents the relationship between the time

Leon jogs in hours, t, and the distance he jogs in miles, d. Complete the table. Graph the

points on the grid.


0

0.25

2.5

1

-3

-4

-1.5-2.0-2.5

Dis

tanc

e (m

iles)

-1.0 -0.5

Time (hours)

0 0.5 1.0 1.5 2.0 2.5-1

0

1

2

3

4

-5

-2

5

x

y


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Name ________________________________________________________ Date _________________________

9. Perry is driving to college. The equation d 5 60t represents the relationship between the time

Perry travels in hours, t, and the distance he travels in miles, d. Complete the table. Graph the

points on the grid.


0

1

2

180

-120

-160

-3-4-5

Dis

tanc

e (m

iles)

-2 -1

Time (hours)

0 1 2 3 4 5-40

0

40

80

120

160

-200

-80

200

x

y


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10. Elesha and Jada are making greeting cards to send to the children’s hospital. Jada makes 2 cards

before Elesha arrives to help. The equation c 5 2 1 8t represents the relationship between the

time Elesha and Jada make cards in hours, t, and the number of cards they make, c. Complete the

table. Graph the points on the grid.

Time (hours) Number of Cards

0

0

0.5

1

-6

-8

Num

ber

of C

ard

s

Time (hours)

0

-2

0

2

4

6

8

-10

-4

10

-1.5-2.0-2.5 -1.0 -0.5 0.5 1.0 1.5 2.0 2.5

x

y


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Name ________________________________________________________ Date _________________________

11. Ling leaves her home and walks for 15 minutes to the park. After she gets to the park, she

resets her pedometer to 0 and continues to walk at the same speed. The equation d 5 2t 2 0.5

represents the relationship between the time Li walks in hours, t, and the distance she walks in the

park in miles, d. Complete the table. Graph the points on the grid.


0

0

0.5

0.75

-1.5

-2.0

Dis

tanc

e (m

iles)

Time (hours)

0

-0.5

0

0.5

1.0

1.5

2.0

-2.5

-1.0

2.5

-1.5-2.0-2.5 -1.0 -0.5 0.5 1.0 1.5 2.0 2.5

x

y


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Pony ExpressInterpreting the Standard Form of a Linear Equation

Problem SetWrite an expression to represent each problem situation. Evaluate the expression to answer the

question.

1. Aiko is walking 2 miles per hour. How far will she walk in 3 hours?

Let x equal the number of hours Aiko walks.

The expression 2x represents the distance Aiko walks in miles.

2x 5 2(3)

5 6 miles

Aiko will walk 6 miles in 3 hours.

2. Isabel is jogging 4 miles per hour. How long will it take her to jog 6 miles?


Name ________________________________________________________ Date _________________________


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3. Chen is biking 6 miles per hour. How far will he travel in 2 hours?

4. Lamar is sketching people’s faces at the spring carnival. He can create 6 sketches per hour.

How many sketches can he create in 4 hours?


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Name ________________________________________________________ Date _________________________

5. Luis is shoveling snow from driveways in his neighborhood to save money for college. He can

shovel 2 driveways per hour. How long will it take Luis to shovel 8 driveways?

6. Darell is mowing lawns to save money for summer vacation. He can mow 1.5 lawns per hour.

How many lawns can he mow in 6 hours?


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Write an expression to represent each problem situation.

7. Eva and Sofia are participating in a relay for charity. Eva jogs 4 miles per hour. Sofia walks

2 miles per hour. Write an expression that represents the distance that Eva and Sofia travel

during the relay.

Let x equal the number of hours Eva jogs.

The expression 4x represents the distance Eva jogs in miles.

Let y equal the number of hours Sofia walks.

The expression 2y represents the distance Sofia walks in miles.

The expression 4x 1 2y represents the distance that Eva and Sofia travel during the relay.

8. Nina and Olivia are taking turns painting portraits at the spring carnival. Nina paints 3 portraits

per hour. Olivia paints 2 portraits per hour. Write an expression that represents the number of

portraits that Nina and Olivia paint during the carnival.


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Name ________________________________________________________ Date _________________________

9. Teresa and Juanita volunteer to take turns making signs for the football game. Teresa makes

8 signs per hour. Juanita makes 6 signs per hour. Write an expression that represents the number

of signs that Teresa and Juanita make for the football game.

10. Geraldo and Raul are participating in a relay for charity. Geraldo rides his bike 6 miles per hour.

Raul rides his bike 5 miles per hour. Write an expression that represents the distance that Geraldo

and Raul travel during the relay.


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11. Nelson and Ronna volunteer to take turns cleaning up the bike path at the park. Nelson cleans

1 mile per hour. Ronna cleans 2 miles per hour. Write an expression that represents the distance

that Nelson and Ronna clean.

12. Denisa and Tonya take turns making bead necklaces to sell at a school fundraiser. Denisa makes

2 necklaces per hour. Tonya makes 3 necklaces per hour. Write an expression that represents the

number of necklaces that Denisa and Tonya make for the school fundraiser.


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Name ________________________________________________________ Date _________________________

Write an equation to represent each problem situation. Solve the equation to answer the question.

Check your answer.

13. The expression 3x 1 2y represents the distance that Shanise and Kiana travel during a 12 mile

relay for charity. Let x represent the number of hours Shanise walks and let y represent the number

of hours that Kiana walks. If Shanise walks for 2.5 hours, how many hours must Kiana walk?

Check:

3x 1 2y 5 12 3x 1 2y 5 12

3(2.5) 1 2(2.25) 0 12

7.5 1 4.5 0 12

12 5 12

3(2.5) 1 2y 5 12

7.5 1 2y 5 12

2y 5 4.5

y 5 2.25

Kiana must walk 2.25 hours.


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14. The expression 2x 1 4y represents the number of portraits that Nina and Olivia paint while taking

turns at the spring carnival. They expect to paint 30 portraits at the carnival. Let x equal the

number of hours Nina paints. Let y equal the number of hours Olivia paints. If Olivia paints for

4.5 hours, how long must Nina paint to complete the 30 portraits?

15. The expression 5x 1 6y represents the number of signs that Joelle and Mattie make for the

basketball game. They plan to take turns to make 25 signs. Let x equal the number of hours

Joelle makes signs. Let y equal the number of hours Mattie makes signs. If Joelle makes signs for

2 hours, how long must Mattie make signs?


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Name ________________________________________________________ Date _________________________

16. The expression 6x 1 5.5y represents the distance that Carlos and Leon travel during a 20 mile

relay for charity. Let x equal the number of hours Carlos rides his bike. Let y equal the number of

hours Leon rides his bike. If Leon rides his bike for 2 hours, how long must Carlos ride his bike to

complete the relay?


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17. The expression 1.5x 1 2y represents the distance that Perry and Ty cover while volunteering to

clean up the bike path at the park. The bike path is 8 miles long. Let x equal the number of hours

Perry cleans the bike path. Let y equal the number of hours Ty cleans the bike path. If Perry cleans

for 3 hours, how long must Ty clean?

18. The expression 4x 1 3.5y represents the number of necklaces that Denisa and Tonya make for the

school fundraiser. They plan to make 30 necklaces. Let x equal the number of hours Denisa makes

necklaces. Let y equal the number of hours Tonya makes necklaces. If Tonya makes necklaces for

4 hours, how long must Denisa make necklaces?


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Name ________________________________________________________ Date _________________________

Slopes, Forms, Graphs, and InterceptsConnecting the Standard Form with the Slope-Intercept Form of Linear Functions

Problem SetComplete each table using the equation in standard form to determine the x-intercept and y-intercept.

Calculate the slope. Graph the equation.

1. 2x 1 4y 5 12

x y Work

0 3

2x 1 4y 5 12

2(0) 1 4y 5 12

4y 5 12

y 5 3

6 0

2x 1 4y 5 12

2x 1 4(0) 5 12

2x 5 12

x 5 6


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y-intercept: (0, 3)

-6

-8

0

-2

0

2

4

6

8

-10

-4

10

-6-8-10 -4 -2 2 4 6 8 10

y

x

x-intercept: (6, 0)

slope 5 3 2 0 ______ 0 2 6

5 3 ___ 26

5 2 1 __ 2

2. 3x 2 5y 5 30

x y Work

0

0


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Name ________________________________________________________ Date _________________________

-6

-8

0

-2

0

2

4

6

8

-10

-4

10

-6-8-10 -4 -2 2 4 6 8 10

y

x

3. 4x 1 2y 5 14

x y Work

0

0


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-6

-8

0

-2

0

2

4

6

8

-10

-4

10

-6-8-10 -4 -2 2 4 6 8 10

y

x

4. 3x 2 4y 5 224

x y Work

0

0


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Name ________________________________________________________ Date _________________________

-6

-8

0

-2

0

2

4

6

8

-10

-4

10

-6-8-10 -4 -2 2 4 6 8 10

y

x

5. 22x 1 3y 5 27.5

x y Work

0

0


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-6

-8

0

-2

0

2

4

6

8

-10

-4

10

-6-8-10 -4 -2 2 4 6 8 10

y

x

6. 2x 2 0.5y 5 4

x y Work

0

0


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Name ________________________________________________________ Date _________________________

-6

-8

0

-2

0

2

4

6

8

-10

-4

10

-6-8-10 -4 -2 2 4 6 8 10

y

x

Convert each equation in standard form to slope-intercept form.

7. 5x 1 6y 5 60

5x 1 6y 5 60

5x 2 5x 1 6y 5 25x 1 60

6y 5 25x 1 60

6y

___ 6

5 25x 1 60 _________ 6

y 5 2 5 __ 6 x 1 10

8. 2x 1 8y 5 216


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9. 210x 1 15y 5 45

11. 18x 2 3y 5 6

10. 8x 1 2y 5 14

12. 3x 1 2y 5 10


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Name ________________________________________________________ Date _________________________

Convert each equation in slope-intercept form to standard form.

13. y 5 1 __ 4

x 1 9

y 5 1 __ 4

x 1 9

4y 5 4 ( 1 __ 4 x 1 9 )

4y 5 x 1 36

2x 1 4y 5 x 2 x 1 36

2x 1 4y 5 36

15. y 5 3x 2 2

14. y 5 28x 1 3

16. y 5 2 2 __ 3 x 1 1


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17. y 5 2 5 __ 2 x 2 6 18. y 5 29x 2 2


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The Journey Starts with a Single Step—But There Are Many Steps After That!Intervals of Increase, Decrease, and No Change

VocabularyChoose the term or phrase from the box that correctly completes each sentence.

constant function increasing function decreasing function

interval of increase interval of decrease constant interval

1. When the value of a dependent variable decreases as the independent variable increases, the

function is said to be a(n) .

2. When both the dependent and independent values of a function increase, the function is said to

be a(n) .

3. When a function is decreasing for some values of the independent variable, it is said to have

a(n) .

4. When the dependent variable does not change as the independent value of a function increases,

the function is said to be a(n) .

5. When a function is constant for some values of the independent variable, it is said to have

a(n) .

6. When a function is increasing for some values of the independent variable, it is said to have

a(n) .


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Problem SetIdentify each function displayed in each graph as an increasing function, a decreasing function, or a

constant function.

1. y

x

2. y

x

decreasing function

3. y

x

4. y

x


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Name ________________________________________________________ Date _________________________

5. y

x

6. y

x

Identify each interval of increase, the interval of decrease, and the constant interval as appropriate for

the function shown in each graph.

7.

00

2

1

4

3

6

7

5

8

9

10

21 43 65 87 109

y

x

Constant interval: The function is constant

from 0 to 3.

Interval of increase: The function is

increasing from 3 to 5.5.

Interval of decrease: The function is

decreasing from 5.5 to 8.5.


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8.

00

20

10

40

30

60

70

50

80

90

100

2010 4030 6050 8070 10090

y

x

9.

-6

-8

0

-2

0

2

4

6

8

-10

-4

10

-6-8-10 -4 -2 2 4 6 8 10

y = |x - 4|

y

x


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Name ________________________________________________________ Date _________________________

10.

-6

-8

0

-2

0

2

4

6

8

-10

-4

10

-6-8-10 -4 -2 2 4 6 8 10

y

x

y = -|x + 2|

11.

00

4

2

8

6

12

14

10

16

18

20y

x42 86 1210 1614 2018


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12.

00

8

4

16

12

24

28

20

32

36

40

84 1612 2420 3228 4036

y

x

Define variables and write an equation (or equations) to represent the problem situation. Graph the

equation (or equations).

13. Noah walks from home to school at a rate of 5 feet per second. It takes Noah 15 minutes to walk

to school. Write an equation that represents Noah’s distance from home. Graph the equation.

Let t 5 time in seconds

00

1000

Dis

tanc

e Fr

om H

ome

(in fe

et)

500

2000

1500

3000

3500

2500

4000

4500

5000

200100 400

Time (in seconds)

300 600500 800700 1000900

y

x

Let d 5 distance from home in feet

15 minutes 5 15(60)

5 900 seconds

d 5 5t

d 5 5(900)

d 5 4500


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Name ________________________________________________________ Date _________________________

14. Mario is at school, 3500 feet from his home. He stays there for 2 hours. Write an equation that

represents Mario’s distance from home. Graph the equation.

00

1000

500

2000

1500

3000

3500

2500

4000

4500

5000

1 2 3 4 5

y

x


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15. Hector is at school, 7200 feet from home. He leaves school and rides his bike home at

a rate of 12 feet per second. Write an equation that represents Hector’s distance from home.

Graph the equation.

0 1000

1600

800

3200

2400

4800

5600

4000

6400

7200

8000

200 300 400 500 600 700 800 900 1000

y

x


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Name ________________________________________________________ Date _________________________

16. Rita walks from home to the store at a rate of 6 feet per second. It takes her 10 minutes to walk

to the store. After arriving at the store, she stays for 30 minutes. Write an equation that represents

Rita’s distance from home. Graph the equation.

0 4000

800

400

1600

1200

2400

2800

2000

3200

3600

4000

800 1200 1600 2000 2400 2800 3200 3600 4000

y

x


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17. Elena is at Lea’s house, which is 3600 feet from Elena’s home. Elena leaves Lea’s house and

walks in the direction toward her home at a rate of 5 feet per second. After 8 minutes, she stops

at Cristina’s house. She stays at Cristina’s house for 30 minutes. Write an equation that represents

Elena’s distance from home. Graph the equation.

0 4000

800

400

1600

1200

2400

2800

2000

3200

3600

4000

800 1200 1600 2000 2400 2800 3200 3600 4000

y

x


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Name ________________________________________________________ Date _________________________

18. Nina is at her friend Maria’s house 9000 feet from home. She stays at Maria’s house for 1 hour.

Nina then rides her bike home at a rate of 10 feet per second. Write an equation that represents

Nina’s distance from home. Graph the equation.

0 4500

1800

900

3600

2700

5400

6300

4500

7200

8100

9000

900 1350 1800 2250 2700 3150 3600 4050 4500

y

x


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Piecewise FunctionsDeveloping the Graph of a Piecewise Function

VocabularyDefine the term in your own words.

1. piecewise function

Problem SetWrite a piecewise function from each table or context.

1. Minutes 0 1 10 20 40 41 50

Gallons of Water in Tub 0 2 20 40 40 36 0

2x, 0 # x # 20

f(x) 5 40, 20 , x # 40

200 2 4x, 40 , x # 50


Name ________________________________________________________ Date _________________________


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2. At 10:00, Sheila biked to Jill’s house. She stayed at Jill’s for an hour. Then, she biked back home.

Sheila can bike 10 miles per hour uphill and 20 miles per hour downhill. (Hint: Use minutes as the

x-value.)

Sheila’s house

10 Miles

Jill’s house

3. Kyle saved $4 per day for 30 days. Then, he spent $5 a day for 8 days. After that he started saving

again at a rate of $3 per day for 22 days.

4. Hours 0 2 5 6 7 8 10

Miles Driven 0 140 350 395 460 525 655


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Name ________________________________________________________ Date _________________________

5. Miles received a $50 gift card to an online music store from his aunt. He decided to spend a certain

amount each day to extend his enjoyment of the gift card. For the first three days, he set his limit

for $5 per day. Then, he was worried it wouldn’t last long enough at that rate, so he changed his

limit to $3 per day until he had $2 left. Then, he used the last $2 on the final day.

6. Seconds 5 10 15 16 20 21 30 31 50

Jump Rope Jumps 15 30 45 49 65 70 115 118 175

7. Kara is a triathlete. It took her 15 minutes to swim, 80 minutes to bike, and 40 minutes to run

one race.

1.5 km 40 km 10 km


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8. Days 0 5 10 17 18 20 21

Calling Card Minutes 100 70 40 40 30 10 0

Graph each piecewise function from the table or context.

9. Minutes 0 1 10 20 40 41 50

Gallons of Water in Tub 0 2 20 40 40 36 0

Variable Quantity Upper Bound Lower Bound Interval

Minutes (x) 50 0 5

Galons of Water in Tub f(x) 50 0 5

x2015

5

Gal

lons

of W

ater

in T

ub

Minutes

10

15

20

25 30 35 40 45 501050

y

25

30

35

40

45

50


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Name ________________________________________________________ Date _________________________

10. At 10:00, Sheila biked to Jill’s house. She stayed at Jill’s for an hour. Then, she biked back home.

Sheila can bike 10 miles per hour uphill and 20 miles per hour downhill. (Hint: Use minutes as the

x-value.)

Sheila’s house

10 Miles

Jill’s house


Minutes (x) 150 0 15

Distance from Home f(x) 10 0 1

x

y


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11. Kyle saved $4 a day for 30 days. Then, he spent $5 a day for 8 days. After that, he started saving

again at a rate of $3 a day for 22 days.


Days (x) 60 0 10

Money f(x) 150 0 25

x

y


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Name ________________________________________________________ Date _________________________

12. Hours 0 2 5 6 7 8 10

Miles Driven 0 140 350 395 460 525 655


Hours (x) 10 0 1

Miles f(x) 700 0 100

x

y


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13. Miles received a $50 gift card to an online music store from his aunt. He decided to spend a

certain amount each day to extend his enjoyment of the gift card. For the first three days, he set

his limit for $5 a day. Then, he was worried it wouldn’t last long enough at that rate, so he changed

his limit to $3 a day until he had $2 left. Then he used the last $2 on the last day.


Days (x) 20 0 3

Money f(x) 50 0 5

x

y


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Name ________________________________________________________ Date _________________________

14. Seconds 5 10 15 16 20 21 30 31 50

Jump Rope Jumps 15 30 45 49 65 70 115 118 175


Seconds (x) 50 0 5

Jumps f(x) 250 0 25

x

y


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15. Kara is a triathlete. It took her 15 minutes to swim, 80 minutes to bike, and 40 minutes to

run one race.

1.5 km 40 km 10 km


Minutes (x) 200 0 20

Kilometers f(x) 55 0 5

x

y


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Name ________________________________________________________ Date _________________________

16. Days 0 5 10 17 18 20 21

Calling Card Minutes 100 70 40 40 30 10 0


Days (x) 21 0 5

Minutes f(x) 100 0 10

x

y


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Documents

Problem Set - Chamblee Middle Schoolchambleems.dekalb.k12.ga.us/Downloads/Student Skills Practice Ch… · Luis is shoveling snow from driveways in his neighborhood to save money