georgia performance 12c using slopes and...

ex plo rat i o n

Using Slopes and Intercepts12C

On the graph below, 40 is called the y-intercept and 8 is calledthe x-intercept.

Copyright © by Holt, Rinehart and Winston. 385 Holt MathematicsAll rights reserved.

210 3 4 5 6 7 8 9 10

45

40

35

30

25

20

15

10

5

y

x

1. How do the rise and run compare to the intercepts?

2. Find the slope of the line by dividing the y-intercept by the x-intercept and then changing the sign of the quotient.Express the slope as a fraction in simplest form.

3. Consider the triangle drawn along the dashed lines belowthe line. Divide the vertical distance (20) by the horizontaldistance (4), change the sign, and then compare thisfraction with the fraction you found in Problem 2.

Think and Discuss

4. Explain how to calculate the slope of a line using the x- andy-intercepts.

5. Explain how to calculate the slope of a line using any twopoints on the line.

Georgia Performance

Standards

M8A3.i, M8A4.a,M8A4.b, M8A4.c,M8A4.d, M8A4.f

Activity 1

Find the x-intercept and y-intercept of the linear equation 2x � y � 8.Use the intercepts to graph the equation.

Step 1 Find the x-intercept by solving for x when y � 0.

Solve 2x � 0 � 8 for x.

x �

Step 2 Find the y-intercept by solving for y when x = 0.

Solve 2(0) � y � 8 for y.

y �

Step 3 Plot the x-intercept and y-intercept on the graph below. Drawthe line of the equation through the two points.


Hands-On Lab 1Using Slopes and Intercepts12C

LESSON

Name Date Class


Hands-On Lab 1Using Slopes and Intercepts, continued12C

LESSON

Name Date ClassName Date ClassName Date Class

Think and Discuss

1. How would you find the x-intercept and y-intercept of anequation that is not written in standard form, such as 2y � 10 � 5x? Find the x-intercept and y-intercept of this equation.

2. Write the equation 4 � 3x � y in standard form.

Try This

1. Graph each of the following linear equations on the graph belowby finding the x-intercept and y-intercept of each. How is theslope of the two lines different?

Equation 1: x � 3y � 9

Equation 2: x � 3y � 9

Name Date Class


Hands-On Lab 2Using Slopes and Intercepts12C

LESSON

Name Date Class

Activity 1

Write the equation in slope-intercept form and graph the line.

4x � y � 12

Step 1 Subtract 4x from both sides.

�4x � 4x � y � 12 � 4x

y � 12 � 4x

Step 2 Rewrite the equation to match slope-intercept form.

y � �4x � 12

What is the y-intercept of the equation?

What is the slope of the equation?

Step 3 Graph the line on a separate sheet of graph paper. To graphthe equation, plot the y-intercept. Then use the slope of theline to plot another point on the line. The slope is negative sothe line will slant downward from left to right.


Hands-On Lab 2Using Slopes and Intercepts, continued12C

LESSON

Name Date Class

Think and Discuss

1. How can you find the equation of a line if you know two pointson the line?

2. For every 1 hour that Emily babysits, she earns $7.00. Write anequation in slope-intercept form to describe this situation.

Try This

1. Jaden’s parents gave him $50 to start a savings account. Eachweek he has to put $5.00 of his allowance into his savingsaccount. Write an equation in slope-intercept form for the line thatdescribes how much money Jaden has in his savings account.

What is the slope of the line?

What is the y-intercept of the line?

Draw the line on the graph below.

x

O

Weeks1 2 3 4 5 6 7 8 9 10

90

70

Mo

ney

in S

avin

gs

Acc

ou

nt

($)

100

80

60

50

y

Name Date Class


Name Date Class

Review for MasteryUsing Slopes and Intercepts12C

LESSON

x-intercept: the x-coordinate of the point at which a line crosses the x-axis

y-intercept: the y-coordinate of the point at which a line crosses the y-axis

You can find the intercepts of a line from its equation.Then you can use the intercepts to graph the line.

Find the intercepts of the line 3x � 4y � 24.

For the x-intercept, For the y-intercept,let y � 0. let x � 0.

3x � 4y � 24 3x � 4y � 243x � 4(0) � 24 3(0) � 4y � 24

3x � 0 � 24 0 � 4y � 243x � 24 4y � 24

�33x� � �

234� �

44y� � �

244�

x � 8 y � 6The x-intercept is 8. The y-intercept is 6.

Find the intercepts of each line.Draw both graphs on the same grid.

1. 2x � 3y � 12for x-intercept for y-intercept

2x � 3( ) � 12 2( ) � 3y � 12

x � y �

2. 6y � 3x � 6for x-intercept for y-intercept

6( ) � 3x � 6 6y � 3( ) � 6

x � y �

xO

y

(x-intercept, 0)

(0, y-intercept)

xO 8

8

4

4�4

�4

�8

�8

y

3x � 4y � 24

xO 8

8

4

4�4

�4

�8

�8

y


Name Date Class

Review for MasteryUsing Slopes and Intercepts (continued)12C

LESSON

slope-intercept form

y � mx � b

slope y-intercept

In this form, the coefficient of x isthe slope and the constant termis the y-intercept.

To rewrite an equation in slope-interceptform, isolate y.

2x � 3y � �12�2x �2x Subtract 2x.

3y � �2x � 12

�33y� � �

�32�x � �

132� Divide by 3.

y � ��32�x � 4

So, m � � �23

� and b � �4.

Write each equation in slope-intercept form and then find theslope and y-intercept.

3. 3y � 4x � 15 4. 3x � 2y � 6

�3y

� � �4

�x � �15

� Divide by 3. Subtract 3x.

Given two points of a line, you can write its equation.

(2, 5) and (�1, �4)

slope � � ��

41

��

52

� � ��

93� � 3

To find b, substitute the slope and the values from one of thepoints into the slope-intercept equation.

y � mx � b → 5 � 3(2) � b5 � 6 � b

�1 � b

So, the equation for the line that passes through (2, 5) and (�1, �4) is y � 3x �1.

Write the equation of the line that passes through each pair ofpoints in slope-intercept form.

5. (2, 11) and (0, 3) 6. (�1, 3) and (4, �2) 7. (10, 1) and (6, �1)

y2y1x2x1

Homework and PracticeUsing Slopes and Intercepts12C

LESSON


Name Date Class

Find the x-intercept and y-intercept of each line. Use theintercepts to graph the equation.

1. x � y � 5 2. 3x � 2y � 6

Write each equation in slope-intercept form and then find theslope and y-intercept.

3. 2x � y � 4 4. 4x � 3y � �9 5. x � 4y � 8

Write the equation of the line that passes through each pair ofpoints in slope-intercept form.

6. (�1, 7), (4, �3) 7. (2, 5), (�8, 15) 8. (8, 4), (�10, �5)

9. Thad’s father gives him $10 for a passing report card plus $5 forevery grade of A. Write an equation of a line in slope-interceptform to express y, the amount received with x grades of A. Statethe slope, x-intercept, and y-intercept of the equation.

y

xO�4 �2

�2

�4

2

2

4

4

y

xO�4 �2

�2

�4

2

2

4

4

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