# Find the equation of the line which passes through a point and is parallel to the line which passes through two other points

So my problem specifically asks the following: Find the equation of the line which passes through the point $P = (2,-1)$ and is parallel to the line which passes through $Q = (2,0)$ and $R = (1,3)$.

Now, I know that I can find a vector $v = R-Q$, and thus establish a parametric equation. I also know that I can take this to a cartesian equation of the form $a_1x + b_1y = c_1$, and from there , I know that any parallel line is a scalar multiple of $a_1x + b_1y$ where $c_2$ is not a scalar multiple of $c_1.$

However, I'm having trouble relating these concepts and I think maybe the bright minds of SE can help this junior Linear Algebra student figure it out.

• The parametric equation of the line you are looking for is given by $(x,y)=P+t(R-Q)$.You know how to produce a cartesian equation from this. – Jens Schwaiger Apr 18 '18 at 3:39
• Eliminate $t$ by solving for it in both of the parametric equations. – amd Apr 18 '18 at 7:34