Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 2 - Section 2.5 - The Point-Slope Form of the Equation of a Line - Exercise Set - Page 163: 40

Answer

$a.$ A line parallel to the given line has slope $m= -\displaystyle \frac{3}{2}.$ $b.$ A line perpendicular to the given line has slope $m=\displaystyle \frac{2}{3}$

Work Step by Step

If two nonvertical lines are parallel, then they have the same slope. If two nonvertical lines are perpendicular, then the product of their slopes is -1. --- Read the slope from $y=mx+b$ $ 3x+2y=6 \qquad$ ... solve for y $ 2y=-3x+6\qquad$ ... /$\div 2$ $y= -\displaystyle \frac{3}{2}x+3 \quad$ The given line has slope $m= -\displaystyle \frac{3}{2}$. $ -\displaystyle \frac{3}{2}\cdot(\frac{2}{3})=-1$ $a.$ A line parallel to the given line has slope $m= -\displaystyle \frac{3}{2}.$ $b.$ A line perpendicular to the given line has slope $m=\displaystyle \frac{2}{3}$
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