Are these parallel, perpendicular, or neither. Y = - 1/4x + 10 and - 2x+8y=6

Get the equations in the same form.

-2x + 8y = 6

Add 2x to both sides.

8y = 2x + 6

Divide both sides by 8.

y = 1/4x + 3/4

y = - 1/4x + 10

y = 1/4x + 3/4

They are neither perpendicular or parallel. If it were parallel, both slopes would be 1/4x or - 1/4x, not different. If it were perpendicular, one of the slopes would have to be - 1/4x or 1/4x and 4x or - 4x.