Answer
$y=-\dfrac{3}{5}x+\dfrac{28}{5}$
Work Step by Step
Using $y-y_1=m(x-x_1)$ or the Point-Slope form where $m$ is the slope and $(x_1,y_1)$ is a point on the line, then the equation of the line with the given slope equal to $
-\dfrac{3}{5}
$ and with the given point $\left(
-4,8
\right)$ is
\begin{array}{l}
y-8=-\dfrac{3}{5}(x-(-4))
\\\\
y-8=-\dfrac{3}{5}(x+4)
\\\\
y-8=-\dfrac{3}{5}x-\dfrac{12}{5}
\\\\
y=-\dfrac{3}{5}x-\dfrac{12}{5}+8
\\\\
y=-\dfrac{3}{5}x-\dfrac{12}{5}+\dfrac{40}{5}
\\\\
y=-\dfrac{3}{5}x+\dfrac{28}{5}
.\end{array}
