Intermediate Algebra (6th Edition)

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

Chapter 3 - Review: 96

Answer

$f(x)=-\dfrac{3}{2}x-1$

Work Step by Step

Using the properties of equality, the given equation, $ 2x-3y=6 ,$ is equivalent to \begin{array}{l} -3y=-2x+6 \\\\ y=\dfrac{-2}{-3}x+\dfrac{6}{-3} \\\\ y=\dfrac{2}{3}x-2 .\end{array} Using $y=mx+b$, where $m$ is the slope, the slope of the given line is \begin{array}{l} m=\dfrac{2}{3} .\end{array} Using $m= -\dfrac{3}{2} $ (negative reciprocal slope since the lines are perpendicular) and the given point $( -4,5 ),$ then the equation of the line is \begin{array}{l} y-5=-\dfrac{3}{2}(x-(-4)) \\\\ y-5=-\dfrac{3}{2}(x+4) \\\\ y-5=-\dfrac{3}{2}x-6 \\\\ y=-\dfrac{3}{2}x-6+5 \\\\ y=-\dfrac{3}{2}x-1 .\end{array} In function notation, this is equivalent to $ f(x)=-\dfrac{3}{2}x-1 .$
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