Conditions for Homogeneity

Theorem

Straight Line

The line $L = \alpha_1 x_1 + \alpha_2 x_2 = \beta$ is homogeneous if and only if $\beta = 0$.

Plane

The plane $P = \alpha_1 x_1 + \alpha_2 x_2 + \alpha_3 x_3 = \gamma$ is homogeneous if and only if $\gamma = 0$.