Answer
$y=-\dfrac{1}{5}x+\dfrac{3}{5}$
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{1}{5}
$ and with the given point $\left(
-2,1
\right)$ is
\begin{array}{l}
y-1=-\dfrac{1}{5}(x-(-2))
\\\\
y-1=-\dfrac{1}{5}(x+2)
\\\\
y-1=-\dfrac{1}{5}x-\dfrac{2}{5}
\\\\
y=-\dfrac{1}{5}x-\dfrac{2}{5}+1
\\\\
y=-\dfrac{1}{5}x-\dfrac{2}{5}+\dfrac{5}{5}
\\\\
y=-\dfrac{1}{5}x+\dfrac{3}{5}
.\end{array}