The Slope of a Line
The rise of a line represents the vertical change when moving from one
point to a second point on a line.
The run of a line represents the horizontal change when moving from one
point to a second point on the line.
The slope of a line is the ratio of the rise to the run. It is a number that
describes the steepness of the line.
Definition
Slope of a Line
The slope of the line that passes through two points, (x_{1}, y_{1}) and
(x_{2}, y_{2}), is given by
slope
where x_{1} ≠ x_{2}.
Example 1
Find the slope of the line that passes through the points (2, 7) and (4, 3).
Solution
Note:
When using the slope formula, it does not
matter which point we choose for (x_{1}, y_{1}) and which we choose for (x_{2}, y_{2}).
Example 2
Find the slope of the line that passes through the points (4, 5) and (3, 5).
Solution
Let (x_{1}, y_{1}) = (4, 5) and (x_{2}, y_{2})
= (3, 5). 
m 

Substitute these values in the slope formula. 


Simplify. 


Divide. 

= 0 
Thus, the slope of the line through (4, 5) and (3, 5) is 0.
In fact, the slope of any horizontal line is 0. 


