Intermediate Algebra (6th Edition)

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

Chapter 3 - Review: 94

Answer

$f(x)=-\dfrac{3}{2}x-8$

Work Step by Step

Using the properties of equality, the given equation, $ 3x+2y=8 ,$ is equivalent to \begin{array}{l} 2y=-3x+8 \\\\ y=-\dfrac{3}{2}x+\dfrac{8}{2} \\\\ y=-\dfrac{3}{2}x+4 .\end{array} Using $y=mx+b$, where $m$ is the slope, the slope is \begin{array}{l} m=-\dfrac{3}{2} .\end{array} Using the same slope (since the lines are parallel) and the given point $( -4,-2 ),$ then the equation of the line is \begin{array}{l} y-(-2)=-\dfrac{3}{2}(x-(-4)) \\\\ y+2=-\dfrac{3}{2}(x+4) \\\\ y+2=-\dfrac{3}{2}x-6 \\\\ y=-\dfrac{3}{2}x-6-2 \\\\ y=-\dfrac{3}{2}x-8 .\end{array} In function notation, this is equivalent to $ f(x)=-\dfrac{3}{2}x-8 .$
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