How can I plot a straight line which is in normal form? Take a look at this link.
Suppose, I have the following equation of a straight line:
$$x  \cos\theta+ y \sin \theta=p$$
If we rearrange the equation as follows:
$$y = \frac{p - x\cos\theta}{\sin\theta}$$
we are again stuck with infinite values of $x$. So, what is the benefit of introducing $\theta$ and $p$ here?
How can/should I plot this?

The normal form can be intepreted as follow, let


*

*$p$ the distance between the line and the origin

*$n=(\cos \theta, \sin \theta)$ the normal unitary vector to the line
therefore for any point $OP=(x,y)$ on the line by dot product we have
$$OP\cdot n=(x,y)\cdot (\cos \theta, \sin \theta)=x\cos \theta+y\sin \theta=p$$
Note that for a given line $\theta$ and $p$  are fixed therefore by the following
$$y = \frac{p - x\cos\theta}{\sin\theta}$$
for $\sin \theta \neq 0$ we can find all the points on the line.
