Question

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. y=(-1/4)x+8 and -2x+8y=4

Answer 1

Comparing both the equations with slope-intercept form( y=mx+c), slope of y=(-1/4)x + 8 is m = -1/4 and slope of -2x + 8y = 4 is m'=1/4. For lines to be parallel, their slopes must be same which is not. For lines to be perpendicular, product of their slopes must be -1 which here is 1/4 x -1/4 = -1/16. Hence they are neither parallel nor perpendicular. 

Answer 2

First put the equations into slope intercept form to analyze the slopes.
y= (-1/4)x+8

-2x+8y=4
8y= 2x+4
y= (1/4)x+(1/2)

These two equations are neither because they do not have equivalent slopes or negative reciprocals of the slopes.

Hope this helps.