Question

$$m=\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}}$$

Solve for X_1

$\left\{\begin{matrix}X_{1}=\frac{X_{2}m+Y_{1}-Y_{2}}{m}\text{, }&Y_{2}\neq Y_{1}\text{ and }m\neq 0\\X_{1}\neq X_{2}\text{, }&m=0\text{ and }Y_{2}=Y_{1}\end{matrix}\right.$

Solve for X_2

$\left\{\begin{matrix}X_{2}=\frac{X_{1}m+Y_{2}-Y_{1}}{m}\text{, }&Y_{2}\neq Y_{1}\text{ and }m\neq 0\\X_{2}\neq X_{1}\text{, }&m=0\text{ and }Y_{2}=Y_{1}\end{matrix}\right.$