The equation of a straight line through two points

3 The equation of a straight line through two points

The equation of the line passing through the points with coordinates $A (x_{1}, y_{1})$ and $B (x_{2}, y_{2})$ is given by the following formula.

Key Point 9

The line passing through points $A (x_{1}, y_{1})$ and $B (x_{2}, y_{2})$ is given by

$\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}} or, equivalently y - y_{1} = (\frac{y_{2} - y_{1}}{x_{2} - x_{1}}) (x - x_{1})$

Task!

Find the equation of the line passing through $A (- 7, 11)$ and $B (1, 3)$ .

First apply the formula: $\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}$

$\frac{y - 11}{3 - 11} = \frac{x + 7}{1 + 7}$ .

Simplify this to obtain the required equation:

$y = 4 - x$

Exercises

Find the equation of the line joining $(1, 5)$ and $(- 9, 2)$ .
Find the gradient and vertical intercept of the line joining $(8, 1)$ and $(- 2, - 3)$ .

$y = \frac{3}{10} x + \frac{47}{10}$ .
0.4, $- 2.2$ .