Gradient
Gradient
- The gradient $m$ measures how steep a line is:
$$m = \frac{\text{change in } y}{\text{change in } x} = \frac{\text{rise}}{\text{run}}$$
- Positive gradient → goes up to the right. Negative gradient → goes down to the right.
Practice
Find the gradient of the line through (1, 2) and (4, 11).
(11 − 2)/(4 − 1) = 9/3 = 3.
Practice
A line that goes down as you move to the right has a gradient that is:
Falling to the right means the change in y is negative for a positive change in x.
Practice
Find the gradient of the line through (0, 1) and (2, 7).
(7 − 1)/(2 − 0) = 6/2 = 3.
Worked example
- Find the gradient through $(1, 2)$ and $(4, 11)$.
- Change in $y = 11 - 2 = 9$; change in $x = 4 - 1 = 3$.
- $m = \dfrac{9}{3} = 3$.
You've got it
Key idea
- gradient $m = \dfrac{\text{rise}}{\text{run}} = \dfrac{\text{change in }y}{\text{change in }x}$
- up to the right = positive; down to the right = negative
- through $(1,2)$ and $(4,11)$: $m = \dfrac{9}{3} = 3$