Equation of Straight Line in Plane

Context
Analytic Geometry

Theorem
A line $$L$$ is the set of all $$\left({x_1, x_2}\right) \in \mathbb{R}^2$$, where $$\alpha_1 x_1 + \alpha_2 x_2 = \beta$$, where $$\alpha_1, \alpha_2, \beta \in \mathbb{R}$$ are given, and not both $$\alpha_1, \alpha_2$$ are zero.