Answer
$f(x)=\dfrac{3}{2}x-\dfrac{13}{2}$
Work Step by Step
Expressing the equation $3x-2y=6$ in the slope intercept form $(y=mx+b)$ results to
\begin{array}{l}\require{cancel}
-2y=-3x+6\\
y=\dfrac{-3}{-2}x+\dfrac{6}{-2}\\
y=\dfrac{3}{2}x-3
.\end{array}
The slope of the line above is $m=\dfrac{3}{2}$. Since parallel lines have the same slope, then the parallel line passing through $(3,-2)$ has the same slope, $m=\dfrac{3}{2}$. Using the Point-Slope Form, $y-y_1=m(x-x_1$), the equation of the parallel line is
\begin{array}{l}
y-(-2)=\dfrac{3}{2}(x-3)\\
y+2=\dfrac{3}{2}(x-3)\\
2y+4=3(x-3)
\text{...multiply both sides by 2}\\
2y+4=3x-9\\
2y=3x-13\\
y=\dfrac{3}{2}x-\dfrac{13}{2}
.\end{array}
In function notation, the parallel line has equation $
f(x)=\dfrac{3}{2}x-\dfrac{13}{2}
.$
