Intermediate Algebra (6th Edition)

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

Chapter 3 - Review - Page 196: 73

Answer

parallel

Work Step by Step

Using the properties of equality, the first equation, $ -x+3y=2 ,$ is equivalent to \begin{array}{l} 3y=x+2 \\\\ y=\dfrac{1}{3}x+\dfrac{2}{3} .\end{array} Using $y=mx+b$, where $m$ is the slope, the slope is \begin{array}{l} m_1=\dfrac{1}{3} .\end{array} Using the properties of equality, the second equation, $ 6x-18y=3 ,$ is equivalent to \begin{array}{l} -18y=-6x+3 \\\\ y=\dfrac{-6}{-18}x+\dfrac{3}{-18} \\\\ y=\dfrac{1}{3}x-\dfrac{1}{6} .\end{array} Using $y=mx+b$, where $m$ is the slope, the slope is \begin{array}{l} m_2=\dfrac{1}{3} .\end{array} Since $m_1=m_2,$ then the given lines are $\text{ parallel .}$
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