Parallel lines have equivalent slopes, so since the slope of the given line is -1/4, the slope of the line we want to find is also -1/4.
Substituting into point-slope form and rearranging into slope-intercept form,
[tex]y+1=-\frac{1}{4}(x+8)\\\\y+1=-\frac{1}{4}x-2\\\\\boxed{y=-\frac{1}{4}x-3}[/tex]
