Equation of Straight Line in Plane/Normal Form

Theorem
Let $\LL$ be a straight line such that:
 * the perpendicular distance from $\LL$ to the origin is $p$
 * the angle made between that perpendicular and the $x$-axis is $\alpha$.

Then $\LL$ can be defined by the equation:
 * $x \cos \alpha + y \sin \alpha = p$

Also known as
The normal form of a straight line in the plane is also known as the canonical form.

Some sources refer to it as the $\tuple {p, \alpha}$ form, after the symbols conventionally used to define it.