To determine the best-fit line, you need to determine what is meant by the word "best". Here, we will derive the standard approach which interprets this to mean that the total vertical error between the line and the provided data points is minimized in some fashion. Indeed, this vertical error would be of the form

and would be zero if f(x) exactly interpolated at the given data point. Note, some of these errors will be positive and some will be negative. To avoid any possible cancellation of errors, you can look at taking absolute values (which is tough to deal with algebraically) or by squaring the errors. This second option will be the approach taken here. This is similar to the approach taken earlier when developing formulas for the variance.