# Slope review

CCSS Math: HSF.LE.A.2
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

## What is slope?

Slope is a measure of the steepness of a line.
$\text{Slope} = \dfrac{\text{rise}}{\text{run}}=\dfrac{\Delta y}{\Delta x}$
Want an in-depth introduction to slope? Check out this video.

### Example: Slope from graph

We're given the graph of a line and asked to find its slope.
The line appears to go through the points $(0,5)$ and $(4,2)$.
$\text{Slope}=\dfrac{\Delta y}{\Delta x}=\dfrac{2-5}{4-0}=\dfrac{-3}{4}$
In other words, for every three units we move vertically down the line, we move four units horizontally to the right.

### Example: Slope from two points

We're told that a certain linear equation has the following two solutions:
Solution: $x=11.4 ~~~ y=11.5$
Solution: $x=12.7 ~~~ y=15.4$
And we're asked to find the slope of the graph of that equation.
The first thing to realize is that each solution is a point on the line. So, all we need to do is find the slope of the line through the points $(11.4,11.5)$ and $(12.7,15.4)$.
\begin{aligned} \text{Slope}=\dfrac{\Delta y}{\Delta x}&=\dfrac{15.4-11.5}{12.7-11.4}\\\\ &=\dfrac{3.9}{1.3}\\\\ &=\dfrac{39}{13}\\\\ &=3\end{aligned}
The slope of the line is $3$.