Home > Graphing > Gradient between two points

The gradient between two points is the gradient of the line that passes through them.

Gradient = $\frac{rise}{run}$

The rise is the change is y = $y_2-y_1$

The run is the change is x = $x_2-x_1$

So the gradient = $\frac{y_2-y_1}{x_2-x_1}$

It does not matter if you do the first coordinate minus the second or the other way round provided that you are consistent.

Examples

Find the gradient between $(3, 6)$ and $(7,14)$

gradient = $\frac{14-6}{7-3}=\frac{8}{4}=2$

Find the gradient between $(2,7)$ and $(5,6)$

gradient = $\frac{6-7}{5-2}=-\frac{1}{3}$

Show that the quadrilateral with vertices $A(0,0)$, $B(6,4)$, $C(4,6)$ and $D(1,4)$ is a trapezium.

To be a trapezium the shape must have a pair of parallel lines, which means a pair of lines with the same gradient.

Gradient AB=$\frac{4-0}{6-0}=\frac{2}{3}$

Gradient BC=$\frac{6-4}{4-6}=-1$

Gradient CD=$\frac{6-4}{4-1}=\frac{2}{3}$

Gradient DA=$\frac{4-0}{1-0}=4$

Since AB and CD have the same gradient the shape must be a trapezium