Answer
$ y-2=-3(x+4) \qquad$ ... point-slope form
$ y=-3x-10 \qquad$ ... slope-intercept form
Work Step by Step
$y=\displaystyle \frac{1}{3}x+7$ is in slope-intercept form. Its slope is $m=\displaystyle \frac{1}{3}.$
If two nonvertical lines are perpendicular, then the product of their slopes is $-1.$
$\displaystyle \frac{1}{3}\cdot(-3)=-1$, so a line perpendicular to it
will have slope $m=-3$.
The new line passes through $(x_{1},y_{1})=(-4,2)$
We write the point-slope equation:
$y-y_{1}=m(x-x_{1})$
$ y-2=-3(x+4) \qquad$ ... point-slope form
Simplify to slope-intercept form (solve for y)
$ y-2=-3x-12 \qquad$ ...add $2$
$ y=-3x-10 \qquad$ ... is the slope-intercept form
