The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 4.9: IDENTIFYING PARALLEL AND

PERPENDICULAR LINES, GIVEN AN EQUATION

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To find out if two lines are parallel or perpendicular, write their equations in slope-intercept

form. Then find the slope. If the slopes are the same, the lines are parallel. If the slopes have

different signs and are reciprocals, the lines are perpendicular. Following are facts about

parallel and perpendicular lines:

PARALLEL LINES

• Parallel lines have the same slope.


• They do not intersect.


• All horizontal lines are parallel.


• All vertical lines are parallel.

PERPENDICULAR LINES

• The slopes have opposite signs and are reciprocals.


• Perpendicular lines intersect at right angles.


• A vertical line and a horizontal line are always perpendicular.

DIRECTIONS: Find whether each pair of lines is parallel, perpendicular, or neither.

1. y= 2 x+1;y= 2 x− 4 2. y=x+7;y=−x+ 2


2. 3 y= 2 x+1; 4y= 2 x− 3 4. y=− 2 x+1;y=

1

2

x− 4

5. y=− 2 x;2y+ 4 x= 5 6. y=−

1

4

x;y= 4 x

CHALLENGE:Cheryl looked at the equationsy= 4 x+1andy=− 2 x+1. She

said that the lines were perpendicular because the slopes have opposite

signs. Do you agree with her conclusion? Why or why not?

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.