Intermediate Algebra (6th Edition)

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

Chapter 3 - Test - Page 198: 17

Answer

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

Work Step by Step

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