Answer
$ y+7=-5(x+2) \qquad$ ... point-slope form
$ y=-5x-17 \qquad$ ... slope-intercept form
Work Step by Step
$y=-5x+4$ is in slope-intercept form. Its slope is $m=-5.$
A line parallel to it has the same slope, $m=-5$
and passes through $(x_{1},y_{1})=(-2,-7)$
We write the point-slope equation:
$y-y_{1}=m(x-x_{1})$
$ y+7=-5(x+2) \qquad$ ... point-slope form
Simplify to slope-intercept form (solve for y)
$ y+7=-5x-10 \qquad$ ...add $(-7)$
$ y=-5x-17 \qquad$ ... is the slope-intercept form
