Equation of Straight Line in Plane/Slope-Intercept Form

Theorem
Let $\LL$ be the straight line defined by the general equation:


 * $\alpha_1 x + \alpha_2 y = \beta$

Then $\LL$ can be described by the equation:
 * $y = m x + c$

where:

such that $m$ is the slope of $\LL$ and $c$ is the $y$-intercept.

Also presented as
This equation can also be seen presented as:


 * $y = x \tan \psi + c$

where $\psi$ is the angle that $\LL$ makes with the $x$-axis.

Also known as
The slope-intercept form of the equation of a straight line in the plane is also known as the gradient-intercept form.