Gradient

Gradient as rise over run, positive, negative, zero and undefined gradients, and the gradient between two points.

Rise over run

Gradient

$$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$$

Gradient slider

Bigger numbers mean steeper lines. The sign tells you uphill or downhill.

Example 1●

Find the gradient between $(1, 2)$ and $(4, 11)$.

$m = \dfrac{11 - 2}{4 - 1} = \dfrac{9}{3} = 3$

Example 2●●

Find the gradient between $(-2, 5)$ and $(2, -3)$.

$m = \dfrac{-3 - 5}{2 - (-2)} = \dfrac{-8}{4} = -2$

Flashcards

Gradient formula

$\dfrac{y_2 - y_1}{x_2 - x_1}$

Horizontal line

$m = 0$

Vertical line

Gradient undefined

Practice