text: what is the derivation of the two point formula?   for the equation of a line?  slope is change in y divided by change in x, so subtract y coordinates and x coordinates of the given points (x1,y1) and (x2,y2): (y1-y2)/(x1-x2).    slope on a line is constant, so if (x,y) is any point on the line, then the slope between it and a known point is the same as the slope between 2 known points, so  (y-y1)/(x-x1) = (y1-y2)/(x1-x2)  finally, move the x term over to the right side:  (y-y1) = (y1-y2)/(x1-x2) * (x-x1)