A perceptron takes two inputs and answers yes or no — by checking which side of one line the input lands on.
Each dot is one input — a pair of numbers (x₁, x₂). For every input there is a correct answer, yes or no, shown by the dot's fill.
It computes z = w₁x₁ + w₂x₂ + b and answers yes when z is positive. That rule is a straight line: everything on the shaded side gets a yes, everything else a no. So the weights and bias are the line.
Move the line until every yes dot is inside the shaded zone and every no dot is outside it. Or press Train and let the learning rule do it — it only nudges the line after it gets a dot wrong.
Two of the three questions can be answered this way. Exactly one on cannot — its yes-dots sit on opposite corners, so no straight line can gather them on one side. That is the perceptron's hard limit, and the reason networks stack units into hidden layers.
| input | z = w₁x₁+w₂x₂+b | says | should say |
|---|