Skill: Calculate the slope between two points

Slope tells how much a line rises or falls compared with how far it moves left or right.

Use the formula

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

where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.

Example

Find the slope of the line through $(2,3)$ and $(6,11)$.

Step 1: Identify the coordinates.

Let

$$(x_1,y_1)=(2,3), \qquad (x_2,y_2)=(6,11)$$

Step 2: Substitute into the formula.

$$m=\frac{11-3}{6-2}$$

Step 3: Simplify.

$$m=\frac{8}{4}=2$$

The slope is

$$\boxed{2}$$

This means the line rises $2$ units for every $1$ unit it moves to the right. A positive slope means the line goes upward from left to right. A negative slope means it goes downward. A horizontal line has slope $0$, while a vertical line has an undefined slope because its change in $x$ is $0$.