We are given a set of points ##(x_i , y_i)##. If we want to fit a line to these points which has the form of ##y=a_0+a_1x##, we need to do it in a way which minimizes the total error E:$$E = \sum_{i=1}^n (y_i - a_0 - a_1x_i)^2$$So we set ##\frac{\partial E}{\partial a_0} = 0## and...