Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 3 - Section 3.4 - The Slope of a Line - Exercise Set: 65

Answer

Perpendicular

Work Step by Step

We are given two lines written in the form $y=mx+b$, where m is the slope of the line and the point (0,b) is the y-intercept. $y=f(x)=-3x+6$ and $y=g(x)=\frac{1}{3}x+5$ In order for two lines to be parallel, they must have the same slope. However, $m=-3$ for the first line and $m=\frac{1}{3}$, so they have different slopes and cannot be parallel. Two lines are perpendicular if the product of their slopes is equal to -1. $-3\times\frac{1}{3}=-1$ Therefore, these two lines are perpendicular.
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