The line L given by 5 y+(2 m-4) x-10 m=0 in the x y-plane intersects the rectangle with vertices O(0,0), A(0,6), B(10,6), C(10,0) at D on the line segment O A and E on the line segment B C.
(a) Show that 1 \leq m \leq 3.
(b) Show that the area of quadrilateral A D E B is \frac{1}{3} the area of rectangle O A B C.
(c) Determine, in terms of m, the equation of the line parallel to L that intersects O A at F and B C at G so that the quadrilaterals A D E B, D E G F, F G C O all have the same area.