Answer
$2x-y=12$
Work Step by Step
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form, the equation of the line with slope $2$ and passing through $(5,-2)$ is
\begin{array}{l}
y-(-2)=2(x-5)
\\\\
y+2=2x-10
\\\\
-2x+y=-10-2
\\\\
-2x+y=-12
\\\\
2x-y=12
.\end{array}