Answer
$ y+10=-4(x+8) \qquad$ ... point-slope form
$ y=-4x-42 \qquad$ ... slope-intercept form
Work Step by Step
$y=-4x+3$ is in slope-intercept form. Its slope is $m=-4.$
A line parallel to it has the same slope, $m=-4$
and passes through $(x_{1},y_{1})=(-8,-10)$
We write the point-slope equation:
$y-y_{1}=m(x-x_{1})$
$ y+10=-4(x+8) \qquad$ ... point-slope form
Simplify to slope-intercept form (solve for y)
$ y+10=-4x-32 \qquad$ ...add $(-10)$
$ y=-4x-42 \qquad$ ... is the slope-intercept form
