ure out of the regularization). So when I write $w^Tx$ without a $b$ assume
that there is a constant feature added that is not part of any regularization.

Geometrially, what the formula means is that the decision boundary of a linear
classifier will be a hyperplane in the feature space, where w is the normal vector of that plane.
In the 2d example here, it's just a line separating red and blue. Everything on the right hand side
would be classified as blue by this classifier, and everything on the left-hand