Answer
$f(x)=-\dfrac{3}{2}x+\dfrac{7}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
.$
