## Intermediate Algebra (12th Edition)

$f(x)=-\dfrac{3}{2}x+\dfrac{7}{2}$
$\bf{\text{Solution Outline:}}$ To find the function notation of the given equation, $2y=-3x+7 ,$ solve first for $y.$ Then use $y=f(x).$ $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} 2y=-3x+7 \\\\ \dfrac{2y}{2}=\dfrac{-3x}{2}+\dfrac{7}{2} \\\\ y=-\dfrac{3}{2}x+\dfrac{7}{2} .\end{array} Using $y=f(x),$ the function notation of the equation above is $f(x)=-\dfrac{3}{2}x+\dfrac{7}{2} .$