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:
![-2x+8y=5 \\ 8y=2x+5 \\ y= \frac{2}{8} x+ \frac{5}{8} = \frac{1}{4}x+ \frac{5}{8}](https://tex.z-dn.net/?f=-2x%2B8y%3D5%20%5C%5C%208y%3D2x%2B5%20%5C%5C%20y%3D%20%5Cfrac%7B2%7D%7B8%7D%20x%2B%20%5Cfrac%7B5%7D%7B8%7D%20%3D%20%5Cfrac%7B1%7D%7B4%7Dx%2B%20%5Cfrac%7B5%7D%7B8%7D%20%20)
The second equation has a gradient of 1/4, which is indeed the negative and reversal of -4, therefore the two lines are
perpendicular.