Answer
$y=\dfrac{3}{5}x+\dfrac{42}{5}$
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 $\left(
-4,6
\right)$ is
\begin{array}{l}
y-6=\dfrac{3}{5}(x-(-4))
\\\\
y-6=\dfrac{3}{5}(x+4)
\\\\
y-6=\dfrac{3}{5}x+\dfrac{12}{5}
\\\\
y=\dfrac{3}{5}x+\dfrac{12}{5}+6
\\\\
y=\dfrac{3}{5}x+\dfrac{12}{5}+\dfrac{30}{5}
\\\\
y=\dfrac{3}{5}x+\dfrac{42}{5}
.\end{array}
