Finding the Equation of a Line

To find the equation of a line from its graph:

Find the gradient of the line, m.
Write down the value of the y‑intercept, c.
Substitute into the formula y = mx + c.

Example

Write down the equation of the line shown:

To find the gradient, use:

\[ \text{Gradient} = \frac{\text{Vertical}}{\text{Horizontal}} \] \[ m = \frac{V}{H} \] \[ m = \frac{-4}{2} \] \[ m = -2 \]

or the:

Gradient formula

\[ (x_1,\; y_1) \qquad\qquad (x_2,\; y_2) \] \[ A(-2,\; 6) \qquad\qquad B(2,\; -2) \]

\[ \text{Gradient} = \frac{\,y_2 - y_1\,}{\,x_2 - x_1\,} \] \[ m = \frac{(-2) - 6}{\,2 - (-2)\,} \] \[ m = \frac{-8}{\,2 + 2\,} \] \[ m = \frac{-8}{4} \] \[ m = -2 \]

This gives m = -2.

The y‑intercept is c = 2.

Substitute into y = mx + c:

\[ y = -2x + 2 \]

Back to Straight Line Equations