I have been doing research on how to find a vector that is perpendicular to the a line or a plane. So far, I have been able to find this website:

<http://www.rasmus.is/uk/t/F/Su58k05.htm>

So accordingly for an equation $y=mx+b$

Finding two points that lie on the line:

Let $x=0$, then $y=b$. Let's call this point $A=(0, b)$
Let $x=1$, then $y=m+b$, let's call this point $B=(1, m+b)$

Then

$
\vec{AB}=\begin{pmatrix}
1-0 \\
m+b-b 
\end{pmatrix}
=\begin{pmatrix}
1 \\
m 
\end{pmatrix}$

If I am correct, this vector $\vec{AB}=(1,m)$ is a direction vector that is parallel to the line $y=mx+b$, is that right?

How do I find the normal vector to this line?