Answer
$ y+3=-5(x-2) \qquad$ ... point-slope form
$ y=-5x+7 \qquad$ ... slope-intercept form
Work Step by Step
$y=\displaystyle \frac{1}{5}x+6$ is in slope-intercept form. Its slope is $m=\displaystyle \frac{1}{5}.$
If two nonvertical lines are perpendicular, then the product of their slopes is $-1.$
$\displaystyle \frac{1}{5}\cdot(-5)=-1$, so a line perpendicular to it
will have slope $m=-5$.
The new line passes through $(x_{1},y_{1})=(2,-3)$
We write the point-slope equation:
$y-y_{1}=m(x-x_{1})$
$ y+3=-5(x-2) \qquad$ ... point-slope form
Simplify to slope-intercept form (solve for y)
$ y+3=-5x+10 \qquad$ ...add $(-3)$
$ y=-5x+7 \qquad$ ... is the slope-intercept form
