## Problem on finding a line between two points

Find the line containing the points $(0, 1)$ and $(3, 0)$ by computing a normal vector to the line. Write it in the form $\bfn \cdot \bfx = b$.
• ## Solution

Recall that
We know the line contains $(0,1)$, so we choose $\bfx_0 = (0,1)$.
We now look for a normal vector $\bfn$.
Because $\bfn$ is perpendicular to the line, it must be perpendicular to the vector from $(0,1)$ to $(3,1)$.
Thus, we are looking for a vector perpendicular to $(3,-1)$.
Recall that
So, we take $\bfn = (1, 3)$.
We now compute that $b = \bfn \cdot \bfx_0 = (1,3) \cdot (0,1) = 3$.
The line containing the points $(0,1)$ and $(3,0)$ is $$(1,3) \cdot (x,y) = 3.$$