Answer
$ y-4=-\displaystyle \frac{1}{2}(x-2) \qquad$ ... point-slope form
$ y=-\displaystyle \frac{1}{2}x+5 \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 $(x_{1},y_{1})=(2,4)$
We write the point-slope equation:
$y-y_{1}=m(x-x_{1})$
$ y-4=-\displaystyle \frac{1}{2}(x-2) \qquad$ ... point-slope form
Simplify to slope-intercept form (solve for y)
$ y-4=-\displaystyle \frac{1}{2}x+1 \qquad$ ...add $4$
$ y=-\displaystyle \frac{1}{2}x+5 \qquad$ ... is the slope-intercept form
