Slope

To “read” a slope, you always go from left to right. If the slope is ascending, it has a positive rise, if it is descending, it has a negative rise.

 

Slope is calculated as:

 

Slope = Rise/Run

 

OR

 

m = Rise/Run

 

A slope is negative only when the rise is negative.

 

The simplest way to determine a slope is to count the run and rise. Example below:

 

 

Here you can see that the rise is 5 and the run is 5.

 

5/5 = 1 therefore the slope is 1. When writing this slope in y = mx + b form, do not include the 1, write it like this: y = x  + 0 (do not include 0’s in your answer, this is just for representation).

 

Rate of Change

 

The slope can also be referred to as a rate of change. For example is the slope is 5 (5/1) then the rate of change is 5.

 

Example:

 

Bob rode his bike 20km in 4 hours.

 

20 / 4 = 5

 

This means the slope is (5/1) and that Bob travels 5km per hour.