Parallel vs. Perpendicular

Types of Lines

Characteristics of Lines

Compare the Slopes

1.

• What do you notice about these two lines? ______________________________

• How do the slopes of the lines compare? ____________________________

• What is the product of the slopes of these two lines? _______________________

Write the slope of a line that is parallel to and perpendicular to the given line.

2. m = _______ b = _______

Parallel: = ________Perpendicular: = _________

3.

m = _______ b = _______

Parallel: = ________ Perpendicular: = _________

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

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-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

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4. Which of the following equations are parallel and which are perpendicular?

a. 3 3y x � b. 1

42

y x � �

c. 5 3( 1)y x� � d. 2 4y x � � e. 2 1y x�

Parallel lines: Perpendicular lines:

A. B. C. 5

23

y x � D. 3 65 5

y x �

5. Write an equation in slope-intercept form for a line passing through the point (4, -8) and parallel to .

6. Write an equation in slope-intercept form for a line passing through the point (-3, 1) and perpendicular to

7. Write an equation in slope-intercept form of the line that passes through (-2, 3) and is parallel to

9. Which of the following describes a line passing through (3, 3) that is perpendicular to the line described by .

Algebra I - Unit 4: Topic 1 – Writing Equations of Parallel and Perpendicular Lines

Practice - Equations of Parallel and Perpendicular Lines pp 353-355 Name _________________________________________ Date ____________________ Period _____________ Identify which lines are parallel.

1. . 3 2a y x � �

1. 1

2b y x �

. 2 17c x y� �

. 3 27d x y�

Identify which lines are perpendicular.

2. . 9 3( 1)a y x� �

1. 5

3b y x � �

. 0c y

. 6d x

Tell whether each pair of lines are parallel, perpendicular, or neither.

3. 7 28 7( 4)y x and y x � � � � 4. 1

3 4 ( 3) 13 ( 1)4

y x and y x� � � � �

Write an equation in slope-intercept form for the line that is parallel to the given line and that passes through the given point. 5. 3 7; (0,4)y x � 6. 5 2 10; (4, 5)x y� � 7. 4; (3, 2)x �

Algebra I - Unit 4: Topic 1 – Writing Equations of Parallel and Perpendicular Lines

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9

-8

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-5

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1

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x

y

-5 -4 -3 -2 -1 1 2 3 4 5

-4-3-2-1

123456789

x

y

-5 -4 -3 -2 -1 1 2 3 4 5

-4-3-2-1

123456789

x

y

Write an equation in slope-intercept form for the lines that is perpendicular to the given line and that passes through the given point. 8. 3 4; (6, 2)y x � � � 9. 3 4 8; ( 6,5)x y� � 10. 3; (2, 4)x � �

11. Which describes a line passing through (3, 3) that is perpendicular to the line described by3

25

y x � ?

� � �5 3 6

. 2 . . .3 5 5

a y x b y x c d

12. Write an equation in slope-intercept form for the line that passes through (1, 1) and is perpendicular to the line

graphed below.