The Hypothesis Function

The model itself — the line — is called the hypothesis function. For one feature it is

h(x) = wx + b.

It has two tunable knobs, the parameters the model learns: w, the weight (the slope — how strongly the feature pushes the prediction), and b, the bias (the intercept — the prediction when the feature is zero). "Training" means searching for the w and b that fit best.

Two knobs, every line

The weight tilts the line; the bias slides it up and down. Between them they can reach any straight line. Adjust both and notice their distinct jobs — w controls the steepness, b the height.

The names matter later

"Weight" and "bias" sound grander than "slope" and "intercept", but it's the same idea — and the grander names are the ones that scale. A neuron is exactly h(x) = wx + b with one extra twist, and a network has millions of weights and biases. Learn the two-knob line cold and you've learned the atom every bigger model is built from.