Home > Graphing > Gradient between two points

Gradient between two points

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

Two points

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

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