1994 AHSME Problem 23

In the xy-plane, consider the L-shaped region bounded by horizontal and vertical segments with vertices at (0,0), (0,3), (3,3), (3,1), (5,1) and (5,0). The slope of the line through the origin that divides the area of this region exactly in half is \textbf{(A)}\ \frac{2}{7} \qquad\textbf{(B)}\ \frac{1}{3} \qquad\textbf{(C)}\ \frac{2}{3} \qquad\textbf{(D)}\ \frac{3}{4} \qquad\textbf{(E)}\ \frac{7}{9}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.