Equation of Straight Line in Plane/Normal Form/Proof 1

Proof

 * Straight-line-normal-form.png

Let $A$ be the $x$-intercept of $\LL$.

Let $B$ be the $y$-intercept of $\LL$.

Let $A = \tuple {a, 0}$ and $B = \tuple {0, b}$.

From the Equation of Straight Line in Plane: Two-Intercept Form, $\LL$ can be expressed in the form:
 * $(1): \quad \dfrac x a + \dfrac y a = 1$

Then:

Substituting for $a$ and $b$ in $(1)$: