Except that the straight line is in feature space and not input space; the computations are done using only a kernel function, which takes vectors in the input

Except that the straight line is in feature space and not input space; the computations are done using only a kernel function, which takes vectors in the input space, and computes the dot product in the feature space. This is a very important distinction because while the method is linear in the feature space, it can solve non-linear problems in the input space.