Answer
$ y-4=-2(x-3) \qquad$ ... point-slope form
$ y=-2x+10 \qquad$ ... slope-intercept form
Work Step by Step
If two nonvertical lines are parallel, then they have the same slope.
The given blue line, $y=-2x$, has slope $m=-2.$
So, the line L has slope $m=-2$, and passes through $(x_{1},y_{1})=(3,4)$
We write the point-slope equation:
$y-y_{1}=m(x-x_{1})$
$ y-4=-2(x-3) \qquad$ ... point-slope form
Simplify to slope-intercept form (solve for y)
$ y-4=-2x+6 \qquad$ ...add $4$
$ y=-2x+10 \qquad$ ... is the slope-intercept form
