Feed the neuron one real input x and a constant input of 1. Its weighted sum is exactly a straight line: the input weight is the slope, the bias weight is the intercept. Then pass that sum through an activation function and watch the line bend.
| Neuron | Line y = ax + b | Current value | What it does |
|---|---|---|---|
| input x₁ = x | x | 1.50 | The independent variable, the horizontal axis. |
| input x₀ = 1 | (implicit 1) | 1 | A constant input so the bias weight can act as an offset. |
| weight w₁ | slope a | 1.00 | Tilts the line. Negative flips it; zero makes it flat. |
| bias weight w₀ | intercept b | 0.50 | Shifts the line up or down. Crosses the y-axis at b. |
| sum z = w₁x + w₀ | y | 2.00 | The pre-activation output. With no activation, this is the neuron's output. |
| z = 0 at x = −w₀/w₁ | x-intercept −b/a | −0.50 | Where the line crosses zero. Step, ReLU, sigmoid and tanh all switch behaviour here. |
The 1943 neuron fires 1 when z ≥ 0 and 0 otherwise. The line becomes a yes/no threshold at x = −b/a.
max(0, z). Keeps the line where it is positive and clamps it to 0 elsewhere, putting a kink at the x-intercept.
1 / (1 + e−z). Squashes the line into (0, 1). The slope a sets how sharp the S is; b slides it left or right.
Squashes into (−1, 1), centred on 0. Like sigmoid, it crosses its midpoint exactly where the line crosses zero.