If $m>0$ and the points $(m,3)$ and $(1,m)$ lie on a line with slope $m$, then $m=$
$\text{(A) } 1\quad \text{(B) } \sqrt{2}\quad \text{(C) } \sqrt{3}\quad \text{(D) } 2\quad \text{(E) } \sqrt{5}$
We know that the formula for slope is $m = \frac{y_2-y_1}{x_2-x_1}$
We are give the points $(m,3)$ and $(1,m)$.
Substituting into the slope formula, we get $\frac{m-3}{1-m}$ 
After taking the cross-products and solving, we get $\sqrt{3}$, which is answer choice $\fbox{C}$.