Equation of a line through two points calculator

Two different points determine exactly one line. The calculator writes it in the slope-intercept form y = mx + b. The slope (gradient) m tells you how far the line rises when you move one unit to the right, and the y-intercept b is where the line crosses the y-axis.

If both points have the same x-coordinate, the line is vertical. It has no slope, and its equation is simply x = x₁.

How it works

The calculator works out the slope and the y-intercept using these formulas:

$$m=\frac{y_2-y_1}{x_2-x_1},b=y_1-m\cdot x_1$$

For points A(1, 3) and B(4, 9), first work out the slope. From A to B we move 3 to the right and 6 up:

$$m=\frac{9-3}{4-1}=\frac{6}{3}=2$$

Work out the y-intercept b from either point, for example A. Substitute into y = mx + b:

$$\begin{array}{rcl}3& =& 2\cdot 1+b/-2\\ b& =& 1\end{array}$$

The equation of the line is y = 2x + 1. Check with point B: 2 · 4 + 1 = 9. It works. Other ways of writing a line are described in the article on lines.