Equation of Straight Line in Plane

Theorem
A straight line $L$ is the set of all $\left({x, y}\right) \in \R^2$, where:
 * $\alpha_1 x + \alpha_2 y = \beta$

where $\alpha_1, \alpha_2, \beta \in \R$ are given, and not both $\alpha_1, \alpha_2$ are zero.