answer
y = -8x - 64
finding slope
a perpendicular line has a slope that is the negative reciprocal of the original graph
since the slope of y = [tex]\frac{1}{8} x+4[/tex] is [tex]\frac{1}{8}[/tex], the perpendicular line has a slope of [tex]\frac{-8}{1} =-8[/tex]
values
the equation of a line is y = mx + b
with the point (-8, 0), x = -8 and y = 0
we found the slope to be m = -8
plug in values
y = mx + b
0 = -8(-8) + b
0 = 64 + b
b = -64
final equation
plug m and b into y = mx + b to get
y = -8x - 64
