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:[tex]-2x+8y=5 \\ 8y=2x+5 \\ y= \frac{2}{8} x+ \frac{5}{8} = \frac{1}{4}x+ \frac{5}{8} [/tex]
The second equation has a gradient of 1/4, which is indeed the negative and reversal of -4, therefore the two lines are perpendicular.
