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Copyright © by Holt, Rinehart and Winston. 6 Holt MathematicsAll rights reserved.
Name Date Class
ReteachGraphing Linear Equations12-1
LESSON
The graph of a linear equation is a straight line.
The line shown is the graph of y � �32
�x � 1.
All the points on the line are solutions of the equation.
Each time the x-value increases by 2, the y-valueincreases by 3. So, a constant change in the x-valuecorresponds to a constant change in the y-values.
Each equation has a table of solutions. Indicate the changes inx-values and in y-values. Tell whether the equation is linear.
1. y � 2x � 5 2. y � 2x 3
not linearlinear
x
O 4
4
6
2
2�2�4
y
(�2, �2)
(0, 1)
(2, 4)
(4, 7)
2
3
2
3
2
3y � x � 132
y � 3x � 4
Since a constant change in the x-valuecorresponds to a constant change in they-value, y � 3x � 4 is a linear equation.
y � 3x 2
Since a constant change in the x-valuedoes not correspond to a constantchange in the y-value, y � 3x 2 is not alinear equation.
x �2 �1 0 1 2y �10 �7 �4 �1 2
+1 +1 +1 +1
+3 +3 +3 +3
x �2 �1 0 1 2y 12 3 0 3 12
+1 +1 +1 +1
�9 �3 +3 +9
x �2 �1 0 1 2y �9 �7 �5 �3 �1
+1 +1 +1 +1
+2 +2 +2 +2
x �2 �1 0 1 2y �16 �2 0 2 16
+1 +1 +1 +1
+14 +2 +2 +14
MSM07G8_RESBK_Ch12_3-11.pe 2/15/06 9:43 AM Page 6
Copyright © by Holt, Rinehart and Winston. 7 Holt MathematicsAll rights reserved.
Name Date Class
ReteachGraphing Linear Equations (continued)12-1
LESSON
To graph a linear equation, make a table to find several solutions.Choose x-values that are easy to graph. Substitute each x-valueinto the equation to find the corresponding y-value. Plot yoursolutions and draw a line connecting them.
Complete the table for each equation and then graph the equation.
3. y � 3x � 1
4. y � � �32
�x � 1
x �12
� x � 3 y (x, y)
�4 �12
� (�4) � 3 �5 (�4, �5)
�2 �12
� (�2) � 3 �4 (�2, �4)
0 �12
� (0) � 3 �3 (0, �3)
6 �12
� (6) � 3 0 (6, 0)
x � �32
�x � 1 y (x, y)
�2 � �32
�(�2) � 1 4 (�2, 4)
0 � �32
�(0) � 1 1 (0, 1)
2 � �32
�(2) � 1 �2 (2, �2)
4 � �32
�(4) � 1 �5 (4, �5)
x 3x � 1 y (x, y)
�2 3(�2) � 1 �7 (�2, �7)
0 3(0) � 1 �1 (0, �1)
1 3(1) � 1 2 (1, 2)
3 3(3) � 1 8 (3, 8)
x
O 8
8
4
4�4
�4
�8
�8
y
y � x � 312
x
O 8
8
4
4�4
�4
�8
�8
y
x
O 8
8
4
4�4
�4
�8
�8
y
MSM07G8_RESBK_Ch12_3-11.pe 2/15/06 9:43 AM Page 7
Copyright © by Holt, Rinehart and Winston. 64 Holt MathematicsAll rights reserved.
Copyright © by Holt, Rinehart and Winston. 3 Holt MathematicsAll rights reserved.
Complete the tables for the given equations.
1. y � 3x � 2 2. y � �x � 3
Complete the table for the given equation. Then graphthe equation.
3. 2x � y � 1
4. Is the equation in Exercise 3 linear? Explain. Possible answer:
Yes, the points form a straight line and each time x increases by 1 unit,
y increases by 2 units.
Practice AGraphing Linear Equations12-1
LESSON
x 3x � 2 y (x, y)
�3 3(�3) � 2 �7 (�3, �7)
�2 3(�2) � 2 �4 (�2, �4)�1 3(�1) � 2 �1 (�1, �1)
0 3(0) � 2 2 (0, 2)1 3(1) � 2 5 (1, 5)2 3(2) � 2 8 (2, 8)3 3(3) � 2 11 (3, 11)
x �x � 3 y (x, y)
�3 �(�3) � 3 0 (�3, 0)�2 �(�2) � 3 �1 (�2, �1)�1 �(�1) � 3 �2 (�1, �2)
0 �(0) � 3 �3 (0, �3)1 �(1) � 3 �4 (1, �4)2 �(2) � 3 �5 (2, �5)3 �(3) � 3 �6 (3, �6)
x 2x � 1 y (x, y)
�3 2(�3) � 1 �7 (�3, �7)�2 2(�2) � 1 �5 (�2, �5)�1 2(�1) � 1 �3 (�1, �3)
0 2(0) � 1 �1 (0, �1)1 2(1) � 1 1 (1, 1)2 2(2) � 1 3 (2, 3)3 2(3) � 1 5 (3, 5)
xO 8
8
4
4�4
�4
�8
�8
y
Copyright © by Holt, Rinehart and Winston. 4 Holt MathematicsAll rights reserved.
Practice BGraphing Linear Equations12-1
LESSON
Graph each equation and tell whether it is linear.
1. y � �2x � 5 2. y � �x2 � 1
3. y � x2 � 7 4. y � �12
�x � 1
5. A real estate agent commission may bebased on the equation C � 0.06s � 450,where s represents the total sales. If theagent sells a property for $125,000, what is the commission earned by the agent? Graph the equation and tellwhether it is linear.
$7950; linear
linearnot linear
not linearlinear
x
O 8
8
4
4�4
�4
�8
�8
y
x
O 44
44
22
22�22
�����22
��44
�44
y
x
O 8
8
4
4�4
�4
�8
�8
y
x
O 44
44
22
22�22
�����22
��44
�44
y
y
x
1505500 1000O
10000001
505505
(thousands)
Copyright © by Holt, Rinehart and Winston. 5 Holt MathematicsAll rights reserved.
Practice CGraphing Linear Equations12-1
LESSON
Graph each equation and tell whether it is linear.
1. y � �3x 2. y � x � 5
3. y � �12
�x � 3 4. y � �x2 � 2
5. Mrs. Blanche grades a math test with acurve based on the formula G � 5.5p �10, where G is the curved grade and prepresents the number of problemscorrect. If Sebastian had 10 problemscorrect, Alisha had 12 problems correct,and Miguel had 14 problems correct, whatwas each student’s curved grade? Graphthe equation and tell whether it is linear.
Sebastian: 65; Alisha:
76; Miguel: 87; linear
x
O 4
4
2
2�2
�2
�4
�4
y
x
O 44
44
22
22�22
�����22
��44
�44
y
x
O 8
8
4
4�4
�4
�8
�8
y
x
O 8
8
4
4�4
�4
�8
�8
y
y
50
100
x
O 50 100
Copyright © by Holt, Rinehart and Winston. 6 Holt MathematicsAll rights reserved.
ReteachGraphing Linear Equations12-1
LESSON
The graph of a linear equation is a straight line.
The line shown is the graph of y � �32
�x � 1.
All the points on the line are solutions of the equation.
Each time the x-value increases by 2, the y-valueincreases by 3. So, a constant change in the x-value corresponds to a constant change in the y-values.
Each equation has a table of solutions. Indicate the changes inx-values and in y-values. Tell whether the equation is linear.
1. y � 2x � 5 2. y � 2x 3
not linearlinear
x
O 4
4
6
2
2�2�4
y
(�2, �2)
(0, 1)
(2, 4)
(4, 7)
2
3
2
3
2
3y � x � 132
y � 3x � 4
Since a constant change in the x-valuecorresponds to a constant change in they-value, y � 3x � 4 is a linear equation.
y � 3x 2
Since a constant change in the x-valuedoes not correspond to a constantchange in the y-value, y � 3x 2 is not alinear equation.
x �2 �1 0 1 2y �10 �7 �4 �1 2
+1 +1 +1 +1
+3 +3 +3 +3
x �2 �1 0 1 2y 12 3 0 3 12
+1 +1 +1 +1
�9 �3 +3 +9
x �2 �1 0 1 2y �9 �7 �5 �3 �1
+1 +1 +1 +1
+2 +2 +2 +2
x �2 �1 0 1 2y �16 �2 0 2 16
+1 +1 +1 +1
+14 +2 +2 +14
Copyright © by Holt, Rinehart and Winston. 65 Holt Mathematics
Copyright © by Holt, Rinehart and Winston. 7 Holt MathematicsAll rights reserved.
ReteachGraphing Linear Equations (continued)12-1
LESSON
To graph a linear equation, make a table to find several solutions.Choose x-values that are easy to graph. Substitute each x-valueinto the equation to find the corresponding y-value. Plot yoursolutions and draw a line connecting them.
Complete the table for each equation and then graph the equation.
3. y � 3x � 1
4. y � � �32
�x � 1
x �12
� x � 3 y (x, y)
�4 �12
� (�4) � 3 �5 (�4, �5)
�2 �12
� (�2) � 3 �4 (�2, �4)
0 �12
� (0) � 3 �3 (0, �3)
6 �12
� (6) � 3 0 (6, 0)
x � �32
�x � 1 y (x, y)
�2 � �32
�(�2) � 1 4 (�2, 4)
0 � �32
�(0) � 1 1 (0, 1)
2 � �32
�(2) � 1 �2 (2, �2)
4 � �32
�(4) � 1 �5 (4, �5)
x 3x � 1 y (x, y)
�2 3(�2) � 1 �7 (�2, �7)
0 3(0) � 1 �1 (0, �1)
1 3(1) � 1 2 (1, 2)
3 3(3) � 1 8 (3, 8)
x
O 8
8
4
4�4
�4
�8
�8
y
y � x � 312
x
O 8
8
4
4�4
�4
�8
�8
y
x
O 8
8
4
4�4
�4
�8
�8
y
Copyright © by Holt, Rinehart and Winston. 8 Holt MathematicsAll rights reserved.
ChallengeA Recognition Factor12-1
LESSON
Different kinds of equations have different kinds of graphs. Bystudying the graphs of different kinds of equations, you canlearn to recognize characteristics of the equations.
1. Complete the table of values to graph each equation. Draw all the graphs on thegiven grid. Write each equation near its graph.
a. y � 2x � 1 b. y � x 2 � 1 c. xy � 6
d. x � y � �1
2. Analyze the equations in Exercise 1 and yourgraphs of the equations.Make a conjecture abouthow you might recognizea linear equation withoutgraphing it.
Possible answer: In a linear equation, both variables are raised to the
first power. Also the variable terms are separated by � or �, not x or � .
x y
�4 �7�3 �5�2 �3�1 �1
x y
�1 20 11 22 5
x y
1 62 33 26 1
x y
�5 4�4 3�3 2�2 1 x
O 8
8
4
4�4
�4
�8
�8
y
x � y � �1
y � 2x � 1
y � x2 � 1
y � 6x
Copyright © by Holt, Rinehart and Winston. 9 Holt MathematicsAll rights reserved.
Problem SolvingGraphing Linear Equations12-1
LESSON
1. The distance in feet traveled by afalling object is found by the formulad �16t 2 where d is the distance infeet and t is the time in seconds.Graph the equation. Is the equation linear?
The equation is not linear.
2. The formula that relates Celsius to
Fahrenheit is F � �95
�C � 32. Graph
the equation. Is the equation linear?
The equation is linear.
Wind chill is the temperature that theair feels like with the effect of thewind. The graph below shows thewind chill equation for a wind speedof 25 mph. For Exercises 3–6, refer tothe graph.
3. If the temperature is 40° with a25 mph wind, what is the wind chill?
A 6° 29°
B 20° D 40°
4. If the temperature is 20° with a25 mph wind, what is the wind chill?
3° H 13°
G 10° J 20°
5. If the temperature is 0° with a25 mph wind, what is the wind chill?
A �30° C �15°
�24° D 0°
6. If the wind chill is 10° and there is a25 mph wind, what is the actualtemperature?
F �11° H 15°
G 0° 25°�J�B
�F
�C
Write the correct answer.
0
32
64
96
128
160
256
224
192
10 2 43
Dis
tan
ce(f
t)
Time (s)
O 8
40
60
20
4�4
�20
�8
Fahrenheit
Celsius
Temp. (°F)
Wind Chill (°F)
O 40
404404
202202
202
�202202
�404404�
Copyright © by Holt, Rinehart and Winston. 10 Holt MathematicsAll rights reserved.
This graphic organizer can help you understand linear equations.
DefinitionA linear equation is an equation with solutions
that lie in a straight line when graphed.
Table of ordered pairs for Graph of ordered pairs fory � 3x � 5: y � 3x � 5:
Use the information in the graphic organizer to answer thefollowing questions.
1. What is a linear equation?
an equation with solutions that lie in a straight line 2. Write the linear equation shown in the example above.
y � 3x � 53. How many solutions for the equation are plotted on the graph?
34. How is each ordered pair shown on the graph?
with a point5. Write one of the solutions (ordered pairs) shown on the graph.
(2, 1), (3, 4), or (4, 7)6. What figure is formed when the points on the graph are
connected?
a straight line
Reading StrategiesUse a Graphic Organizer12-1
LESSON
xO 4 5
4
21
3
5
78
2 31
y
6
6
x y (x, y)2 1 (2, 1)
3 4 (3, 4)
4 7 (4, 7)
LinearEquations
MSM07G8_RESBK_Ch12_64-xx.pe 2/15/06 10:30 AM Page 65
