Tell us whether the lines for each pair of equations are parallel, perpendicular, or neither: y=-4x +3; -2x+8y=5

Two lines are parallel if the gradient (i.e. the x coefficient) of them both is the same.
Two lines are perpendicular if the gradient has its sign changed and has it's fraction flipped (i.e. a gradient of 2/3 would become -3/2, and a gradient of 10 would become -1/10)

THe first one is in the correct form already, with a gradient of -4.
Now we need to rearrange the second:
The second equation has a gradient of 1/4, which is indeed the negative and reversal of -4, therefore the two lines are perpendicular.