Answer
$ y-2=\displaystyle \frac{1}{2}(x+1) \qquad$ ... point-slope form
$ y=\displaystyle \frac{1}{2}x+\frac{5}{2} \qquad$ ... slope-intercept form
Work Step by Step
If two nonvertical lines are perpendicular, then the product of their slopes is $-1$.
The given blue line, $y=-2x$, has slope $m=-2.$
So, the line L has slope $m=\displaystyle \frac{1}{2}$,
and passes through $(x_{1},y_{1})=(-1,2)$
We write the point-slope equation:
$y-y_{1}=m(x-x_{1})$
$ y-2=\displaystyle \frac{1}{2}(x+1) \qquad$ ... point-slope form
Simplify to slope-intercept form (solve for y)
$ y-2=\displaystyle \frac{1}{2}x+\frac{1}{2} \qquad$ ...add $2$
$ y=\displaystyle \frac{1}{2}x+\frac{5}{2} \qquad$ ... is the slope-intercept form
