If the lines $y = 3x +1$ and $2y = x + 3$ are equally inclined to the line $y = mx + 4$, find the value of $m$.

Question

$\begin {array} {1 1} (A)\;\large\frac{-1 \pm 5 \sqrt 2}{7} & \quad (B)\;\large\frac{1 \pm 5 \sqrt 2}{7} \\ (C)\;\large\frac{-1 \pm 2\sqrt 5}{7} & \quad (D)\;\large\frac{1 \pm 2\sqrt 5}{7} \end {array}$