From Two Points

To find the equation of a line through two points, first calculate the slope, then use point-slope form with either point. For the line through (1, 2) and (3, 8):

m = (8 - 2)/(3 - 1) = 3

y - 2 = 3(x - 1)

y = 3x - 1

You can use the other point instead, which gives y - 8 = 3(x - 3). Expanding and rearranging gives the same equation, y = 3x - 1, because both points lie on the same line.

For two points with different x-coordinates, calculate the slope, substitute either point into point-slope form, and simplify. If the points have the same x-coordinate, the line is vertical.