Can someone explain to me in detail Short proof Wooldridge 2

Can someone explain to me in detail

Short proof (Wooldridge 2.2) In the simple linear regression model y = b0 +b1x+u, suppose that
E(u) 6= 0. Letting a0 = E(u), show that the model can always be rewritten with the same slope, but a
new intercept and error, where the new error has a zero expected value.

Solution

Sol)

simple linear regression model y = b0 +b1x+u

y=b0 +b1x+u

Now apply Expectation on Both sides

E(y) =E(b0 +b1x+u)

E(y) =E(b0) +E(b1x)+E(u)

E(y) =b0+b1 E(x)+0

y bar= b0+b1 x bar

here slope is b1 and bo is intercept