Intermediate Algebra (6th Edition)

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

Chapter 3 - Review - Page 197: 122



Work Step by Step

Using the properties of equality, the given equation, $ 5x-4y=10 ,$ is equivalent to \begin{array}{l} -4y=-5x+10 \\\\ y=\dfrac{-5}{-4}x+\dfrac{10}{-4} \\\\ y=\dfrac{5}{4}x-\dfrac{5}{2} .\end{array} Using $y=mx+b$, where $m$ is the slope, the slope is \begin{array}{l} m=\dfrac{5}{4} .\end{array} Using $m= -\dfrac{4}{5} $ (negative reciprocal since the lines are perpendicular) and the given point $( -5,7 ),$ then the equation of the line is \begin{array}{l} y-7=-\dfrac{4}{5}(x-(-5)) \\\\ y-7=-\dfrac{4}{5}(x+5) \\\\ y-7=-\dfrac{4}{5}x-4 \\\\ y=-\dfrac{4}{5}x-4+7 \\\\ y=-\dfrac{4}{5}x+3 .\end{array}
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