Gradient of a line

The gradient of a line is defined to be the gradient of any interval within the line.

Example 4

Find the gradient of the line passing through the points:

1. A(1, −4) and B(5, 12)
2. C(6, –5) and D(–4, 2)

Solution

1. The gradient of the interval \(AB =\dfrac{y_2 − y_1}{x_2 − x_1} =\dfrac{12 − 4}{5 −1} = \dfrac{8}{4} = 2\)
   Therefore the gradient of the line AB = 2.
2. The gradient of the interval \(CD =\dfrac{y_2 − y_1}{x_2 − x_1} =\dfrac{2 −(−5)}{−4 − 6} = \dfrac{7}{−10}\)
   Therefore the gradient of the line \(CD = −\dfrac{7}{10}\).