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 R - Elementary Algebra Review - R.3 Introduction to Graphing - R.3 Exercise Set - Page 954: 45



Work Step by Step

Using $y=mx+b$ where $m$ is the slope, the slope of the first equation, \begin{array}{l}\require{cancel} 2x+3y=1 \\\\ 3y=-2x+1 \\\\ y=-\dfrac{2}{3}x+\dfrac{1}{3} \end{array} is $m_1= -\dfrac{2}{3} .$ Using $y=mx+b$ where $m$ is the slope, the slope of the second equation, \begin{array}{l}\require{cancel} 2x-3y=5 \\\\ -3y=-2x+5 \\\\ y=\dfrac{-2}{-3}x+\dfrac{5}{-3} \\\\ y=\dfrac{2}{3}x-\dfrac{5}{3} \end{array} is $m_2= \dfrac{2}{3} .$ Since $m_1\ne m_2$ nor $m_1\cdot m_2\ne-1,$ then the given lines are $\text{ neither }$ parallel nor perpendicular.
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