Mean term in simple linear regression

Question

I am trying to derive the expression for the $E(y_i \epsilon_i)$ in simple linear regression. I substitute using $Cov(X,Y) = E(XY) - E(X)E(Y)$, so $E(y_i \epsilon_i) = Cov(y_i , \epsilon_i)- (E(y_i)E(\epsilon_i))$ and $E(\epsilon_i)=0$, so $E(y_i \epsilon_i) = Cov(y_i , \epsilon_i)$, but I don't know how to deal with it.