# How do you find the parametric equations for a line through a point?

If a line goes through the point $\left({x}_{0} , {y}_{0}\right)$ with the direction $\left(a , b\right)$, then the parametric equation of the line is
$\left\{\begin{matrix}x \left(t\right) = {x}_{0} + a t \\ y \left(t\right) = {y}_{0} + b t\end{matrix}\right.$