Equation of Straight Line in Plane/Two-Point Form/Proof 1

Proof
From the slope-intercept form of the equation of the straight line:


 * $(1): \quad y = m x + c$

which is to be satisfied by both $\tuple {x_1, y_1}$ and $\tuple {x_2, y_2}$.

We express $m$ and $c$ in terms of $\paren {x_1, y_1}$ and $\paren {x_2, y_2}$:

Substituting for $m$ and $c$ in $(1)$: