Slope of a Line
Definition of Slope
The slope of a line is the ratio of the rise to the run when moving from any
point on the line to any other point on the line. This ratio is a number that
describes the steepness of the line.
By tradition, the letter m is used to represent the slope of a line.
Definition — Slope
The slope of the line between two points, (x1, y1) and (x2, y2), is
given by
![](./articles_imgs/1060/slope-10.gif)
where x1 ≠ x2.
Example
Find the slope of the line through the points (-2, 1) and (3, 5).
Solution
It does not matter which point we choose for (x1, y1).
For example,
let (x1, y1) = (-2, 1) and (x2, y2)
= (3, 5). |
m |
![](./articles_imgs/1060/slope-11.gif) |
Substitute the values in the slope formula. |
|
![](./articles_imgs/1060/slope-12.gif) |
Simplify. |
|
![](./articles_imgs/1060/slope-13.gif) |
The slope of the line is
.
![](./articles_imgs/1060/slope-15.gif)
To move from (-2, 1) to (3, 5), the ratio of rise to run is
. |
We obtain the same slope if we choose
(3, 5) for (x1, y1) and (-2, 1) for (x2, y2). |
m |
![](./articles_imgs/1060/slope-11.gif) |
Substitute the values in the slope formula. |
|
![](./articles_imgs/1060/slope-17.gif) |
Simplify. |
|
![](./articles_imgs/1060/slope-18.gif) |
![](./articles_imgs/1060/slope-19.gif)
To move from (3, 5) to (-2, 1), the ratio of rise to run is
.
|