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1The math
\begin{aligned}\mathcal{L}(w,b)&=\tfrac{1}{n}\textstyle\sum_{i}\big(w x_i + b-y_i\big)^2\\ w&\leftarrow w-\eta\,\partial \mathcal{L}/\partial w\end{aligned}

Mean squared error, and one gradient step that moves the line downhill.

Read: Gradient Descent, Visually Explained →
2The code
import numpy as np

w, b, lr = 0.0, 0.0, 0.05
for epoch in range(200):
    err = (w * x + b) - y   # error
    w -= lr * 2 * np.mean(err * x)
    b -= lr * 2 * np.mean(err)
# → w ≈ 1.53, b ≈ 0.77
→
3The output, live Live

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