In the xy-plane, line m passes through the origin and is perpendicular to the line 8x-3y=n, where n is a constant. If the two lines intersect at the point (r, r-2), what is the value of r?

Answer 1

Line m has slope -3/8. So, using the point-slope form,

y-(r-2) = -3/8 (x-r)
or,
3x+8y = 11r-16

Now solve that along with 8x-3y=n and set the intersection to be (r,r-2). Then solve for r in terms of n.

Answer 2

8