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.