Skill: Determine slope from two points

Slope tells you the vertical change for every 1 unit of horizontal change. For two points, use

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

where $m$ is the slope.

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

1. Label the coordinates:

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

2. Substitute the values into the slope formula:

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

3. Simplify:

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

The slope is

$$\boxed{2}$$

This means that for every increase of $1$ in $x$, the value of $y$ increases by $2$. The slope is positive because the line rises from left to right.

Be consistent with the order of the points: subtract the $y$-values in the same order as the $x$-values. A horizontal line has slope $0$; a vertical line has an undefined slope because its horizontal change is $0$.