Parametric equation of a line

Summary

A parametric equation of a line describes its points as the values of a function of one real parameter $t$. The line in $\mathbb{R}^3$ through the point $(x_0, y_0, z_0)$ with the nonzero direction vector $(a, b, c)$ has the parametric equations $$x = x_0 + a t, \quad y = y_0 + b t, \quad z = z_0 + c t, \qquad t \in \mathbb{R}.$$ In vector form, the line through the point $p$ with the direction vector $v \neq 0$ is the set of the points $p + t v$ for $t \in \mathbb{R}$. The same form works in $\mathbb{R}^n$ for each $n \geq 2$.