Using ordered pairs to write the equation of a best-fit line?

Question

How would you use two ordered pairs to write the equation of a best-fit line?

Thank you!

Answer 1

Two ordered pairs determine exactly one line. There's no fitting; it passes through both points. A best-fit line is for three or more points (ordered pairs) that, in general, do not all lie on one line.

I'm almost sure this isn't what you want, but if the two points are (x1, y1) and (x2, y2) then an equation for the line passing through them is

y - y1 = [(y2 - y1)/(x2 - x1)] (x - x1) provided x1≠x2.

If x1 = x2, the equation is x = x1