I am having trouble understanding how linear equations in polar coordinates work.
Say I have two points on the same line: $(1,1)$ and $(3,3)$.
Then for the equation $$b=y-mx,$$ $b=0$ and $m=1$ holds for the two points.
But for the equation $$r=x\cos\theta+y\sin\theta,$$ with $\theta=45\pi/180$, $r$ is different; it's $1.4$ for $(1,1)$ and $4.2$ for $(3,3)$.
I don't understand; shouldn't $r$ be constant?