Answer
$4x-y=-3$
Work Step by Step
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions,
\begin{align*}\require{cancel}
y_1&=
-5
,\\x_1&=
-2
,\\m&=
4
,\end{align*}
is
\begin{align*}\require{cancel}
y-(-5)=4(x-(-2))
\end{align*}
In the form $Ax+By=C,$ the equation above is equivalent to
\begin{align*}
y+5&=4(x+2)
\\
y+5&=4x+8
\\
-4x+y&=8-5
\\
-4x+y&=3
\\
-1(-4x+y)&=(3)(-1)
\\
4x-y&=-3
\end{align*}
