Answer:
y  =  -8x-12
Step-by-step explanation:
We have given an equation of line and a point.
-x+8y=16  and (x,y) =  (-2, 4) 
We have to find the equation of line that is perpendicular -x+8y=16.
y  = mx+c is equation of line where m is slope and c is y-intercept.
8y  =  x+16
y  = 1/8x+2 
Hence, slope of perpendicular line is -8.
y  =  -8x+c is equation of perpendicular line to -x+8y=16.
putting the value of point in above equation , we have
4 = -8(-2)+c
4  =  16+c
c  =  4-16
c  =  -12
hence, y  = -8x-12  is equation of line passes through (-2, 4) and perpendicular to -x+8y=16.