2013 AMC 12B Problem 8

Line l_1 has equation 3x - 2y = 1 and goes through A = (-1, -2). Line l_2 has equation y = 1 and meets line l_1 at point B. Line l_3 has positive slope, goes through point A, and meets l_2 at point C. The area of \triangle ABC is 3. What is the slope of l_3?

\textbf{(A)}\ \frac{2}{3} \qquad \textbf{(B)}\ \frac{3}{4} \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ \frac{4}{3} \qquad \textbf{(E)}\ \frac{3}{2}

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