Equations from points and intercepts

A non-vertical line has constant gradient m=Delta y/Delta x and equation y-y_1=m(x-x_1). Equal changes in x give equal changes in y. Check the coordinates first. Equal x-coordinates give a vertical line x=a; equal y-coordinates give a horizontal line y=b. Otherwise find m, substitute one point, then check the other. Through (1,2), (3,8): m=3, so y-2=3(x-1) and y=3x-1. Through (4,-2), (4,7), the equation is x=4. Check: zero gradient is horizontal; undefined gradient is vertical. Two identical points do not determine a unique line.