Gradient and y = mx + c

Gradient from rise over run and from two points, gradient-intercept form, rearranging equations into y = mx + c and sketching using the gradient and y-intercept.

Gradient

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

Example 1●

Find the gradient through $(-1, 4)$ and $(3, -4)$.

$m = \dfrac{-4 - 4}{3 - (-1)} = \dfrac{-8}{4} = -2$

Gradient-intercept form

Sketch from m and c

Start at the y-intercept, then use the gradient as rise over run.

Example 2●●

Find the gradient and $y$-intercept of $4x + 2y = 10$.

$2y = -4x + 10$

$y = -2x + 5$, so $m = -2$, $c = 5$.

Flashcards

Gradient of $y = -3x + 7$

$-3$

Rearranging tip

Get $y$ alone on one side.

$m = frac{2}{3}$

Across $3$, up $2$.

Practice

Gradient through $(-1, 4)$ and $(3, -4)$?
Give $m$ and $c$ for $4x + 2y = 10$.
Give $m$ and $c$ for $y = -3x + 7$.
Gradient through $(0, 1)$ and $(3, 3)$?
Give $m$ and $c$ for $3x - y = 4$.
Give $m$ and $c$ for $x - 2y = 6$.
A line has gradient $2$ and passes through $(0, 0)$. Find $y$ when $x = 3$.
Which line is steepest?