Reading about support vector machines. The equation of separating hyperplane is given as:
$w^Tx + b = 0$
Now, I am at a loss. Argument $w^Tx $ says (if equal to 0) that cosine of point $x$ and normal vector $w$ is 0, but what if the point is not in the plane going through origin? Then the inner product of $w^Tx$ will be $|w||x|cosQ$ - how is coefficient $b$ is then chosen? In the equation $y = ax + b$ it is clear that coefficient $b$ moves $ax$ up along y-axis. In case of $w^Tx + b$, it moves $w^Tx$ along the $w$ for the distance b? Is my intuition right? Can someone give some intuition?