Skill: Determine slope from a graph

Slope tells how much a line changes vertically for each 1-unit change horizontally. Find it by comparing the rise to the run:

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

Example

Suppose a straight line on a graph passes through the points $(1,2)$ and $(4,8)$.

1. Choose two points on the line.
   Let $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(4,8)$.

2. Find the vertical change, or rise.

$$\text{rise}=y_2-y_1=8-2=6$$

3. Find the horizontal change, or run.

$$\text{run}=x_2-x_1=4-1=3$$

4. Divide the rise by the run.

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

The slope is $\boxed{2}$. This means that for every $1$ unit the line moves to the right, it rises $2$ units.

A line that rises from left to right has a positive slope. A line that falls from left to right has a negative slope, and a horizontal line has slope $0$.