If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Slope review

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.
start text, S, l, o, p, e, end text, equals, start fraction, start text, r, i, s, e, end text, divided by, start text, r, u, n, end text, end fraction, equals, start fraction, delta, y, divided by, delta, x, end fraction
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.
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points zero, five and four, two.
The line appears to go through the points left parenthesis, 0, comma, 5, right parenthesis and left parenthesis, 4, comma, 2, right parenthesis.
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points zero, five and four, two. Both of these points are plotted on the graph.
start text, S, l, o, p, e, end text, equals, start fraction, delta, y, divided by, delta, x, end fraction, equals, start fraction, 2, minus, 5, divided by, 4, minus, 0, end fraction, equals, start fraction, minus, 3, divided by, 4, end fraction
In other words, for every three units we move vertically down the line, we move four units horizontally to the right.
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points zero, five and four, two. Both of these points are plotted on the graph. There is a horizontal dotted segment from zero, five to four, five that is labeled four. There is a vertical dotted segment from four, five to four, two that is labeled negative three.

### Example: Slope from two points

We're told that a certain linear equation has the following two solutions:
Solution: x, equals, 11, point, 4, space, space, space, y, equals, 11, point, 5
Solution: x, equals, 12, point, 7, space, space, space, y, equals, 15, point, 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 left parenthesis, 11, point, 4, comma, 11, point, 5, right parenthesis and left parenthesis, 12, point, 7, comma, 15, point, 4, right parenthesis.
\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.