Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 3 - Introduction to Graphing - Review Exercises: Chapter 3: 55

Answer

Two perpendicular lines can share the same y-intercept as long as their slopes are negative reciprocals of each other (their product is $-1$).

Work Step by Step

RECALL: Two lines are perpendicular to each other if their slopes are negative reciprocals of each other (their product is $-1$). Thus, two lines are perpendicular to each other, regardless of their y-intercepts, as long as their slopes are negative reciprocals of each other. Example: The line $y=-x+3$ has a slope of $-1$. The line $y-x=3$ has a slope of $1$. Since their slopes are negative reciprocals of each other, then these two lines are perpendicular to each other. Note that the two lines have the same y-intercept.
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