One Step Downhill

Gradient descent is run on the mean-squared-error loss

$J(b_0, b_1) = \frac{1}{n}\sum_{i=1}^{n} (b_0 + b_1 x_i - y_i)^2$

with the update rules

$b_0 := b_0 - \eta \frac{2}{n} \sum (\hat{y}_i - y_i), \qquad b_1 := b_1 - \eta \frac{2}{n} \sum (\hat{y}_i - y_i)\,x_i$

The data are the four points

$(1,\,3),\quad (2,\,5),\quad (3,\,4),\quad (4,\,8)$

Training starts at $b_0 = 1$ and $b_1 = 1$ with learning rate $\eta = 0.1$. Both parameters are updated simultaneously, each using the predictions from the starting values.

What are $b_0$ and $b_1$ after exactly one step?