AHSME 1967 Problem 12

If the (convex) area bounded by the x-axis and the lines $y=mx+4$, $x=1$, and $x=4$ is $7$, then $m$ equals: $\textbf{(A)}\ -\frac{1}{2} \textbf{(B)}\ -\frac{2}{3} \textbf{(C)}\ -\frac{3}{2} \textbf{(D)}\ -2 \textbf{(E)}\ \text{none of these}$