Line
In $R_{2}$, we define lines as $y=mx+c$
To describe a line, we need

A point on the line

A vector $d$ in the direction of the line.
A line in $R_{n}$ through a point $P$ with direction $d$, where $d∈R_{n}$ is nonzero, is given by the vector equation $L:x= x_{1}⋮x_{n} =OP+td,t∈R$