With slopes in hand, learning is a loop: compute the loss, get the gradients, step every parameter a little against its gradient, clear the gradients, repeat.

import torch

x = torch.linspace(-1, 1, 20)
y = 3 * x
w = torch.zeros(1, requires_grad=True)
for step in range(200):
    loss = ((w * x - y) ** 2).mean()
    loss.backward()
    with torch.no_grad():
        w -= 0.1 * w.grad
    w.grad.zero_()
print(w.item())  # close to 3

Two details matter. The update happens inside torch.no_grad(), so it is not recorded as part of the model. And gradients add up across backward() calls, so they must be cleared every step.

The step size, the learning rate, decides everything: too small and nothing moves, too large and the loss explodes.

Write fit_line(x, y, lr=0.1, steps=500) that learns w and b for y ≈ w * x + b by gradient descent on the mean squared error, starting from zero, and returns them as floats (w, b).

The explanation opens here once every check passes.