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
.$
