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):

$$m = \frac{8-2}{3-1} = 3$$

$$y-2 = 3\left(x-1\right)$$

$$y = 3x-1$$

You can use the other point instead, which gives $y-8 = 3\left(x-3\right)$. 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.