Well, the answer is "probably not"! How would the calculator know that it had checked a sufficient number of lines and residuals to have arrived at the absolute best choice?

It is more likely that your calculator is using a formula for the best fit regression line, also called the least squares line. Don't get too excited that you have discovered a short cut to finding the best regression lines! Such formulas can be rather messy.

Here is the formula for a linear least squares line, or best fit straight line:
(Remember that the equation of a line is y = mx + b, with m = slope and b = y-intercept.)