Parametric Equation of a Line

Theorem: Parametric Equation of a Line

Every straight line has a parameterisation $l:\mathbb{R}\to {\mathbb{R}}^n$ defined as

$$l(t)=\vec{r}+t\vec{v}$$

for some nonzero vectors $\vec{r},\vec{v}\in {\mathbb{R}}^n$.

PROOF

TODO