Speaking informally, quickly, before my son has to go to piano:
The fact of the dot product, and its relationship to projection into spaces (and distance) is crucial. Taking the equation:
y = Wx + band figuring out how all can be variables of a sort (weights and data)… there is a reversal moving from the (known) data points into the (unknown) space, defined by weights. Once the space is known, predictions can be made…