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.

J= r + 9 because since jessica rode 9 more miles than roger, you add 9 miles to rogers mileage.