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 â€” Slope
The slope of the line between two points, (x_{1}, y_{1}) and (x_{2}, y_{2}), is
given by
where x_{1} ≠ x_{2}.
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 (x_{1}, y_{1}).
For example,
let (x_{1}, y_{1}) = (2, 1) and (x_{2}, y_{2})
= (3, 5). 
m 

Substitute the values in the slope formula. 


Simplify. 


The slope of the line is
.
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 (x_{1}, y_{1}) and (2, 1) for (x_{2}, y_{2}). 
m 

Substitute the values in the slope formula. 


Simplify. 


To move from (3, 5) to (2, 1), the ratio of rise to run is
.
