Blog Post #4: Rate of Change

Today, I am going to teach you about rate of change. Rate of change is the is amount of change that occurs between a y-point and an x-point. To first show this, I will provide the formula. The formula is the same formula as the slope formula, so to most, it will may recognizable.

Rate of Change: delta change= y2-y1/x2-x1

The object is to take any two random x-points in the table, and their corresponding y-points to determine this. In the case of the formula, the x-points are the independent variable and the y-points are the dependent variable. The actual delta symbol is a triangle, but I am unable to do this in the document. Just remember if you see a triangle at the start of the formula on a test, or in your general daily activities, it is asking for the rate of change.

The one interesting thing that rate of change allows you to determine is if a function is linear or not. You are able to do this by solving the rate of change formula for multiple points in a chart or table. If the rate of change after each of the calculations is the same, then you have a constant rate of change. A constant rate of change means the function is linear. In order to better display this, I will show two tables, one having a inconstant rate of change and the other having a constant rate of change. This will also allow you to see how to solve for the rate of change.

Deltachange= 150-75/3-0

Deltachange= 75/3                   

Deltachange= 25

Deltachange= 300-150/6-3

Deltachange= 150/3

Deltachange= 50

This was an example of a function that did not have a constant rate of change. As is stated above, this means that the function is not linear. 

For this, I will use the function on the left.

Deltachange= 6-0/1-0

Deltachange= 6/1

Deltachange= 6

Deltachange= 12-6/2-1

Deltachange= 6/1

Deltachange= 6

Deltachange= 18-12/3-2

Deltachange= 6/1

Deltachange= 6

This was an example of a function that had a constant rate of change so the function is linear. 

Those were examples of how to solve for the rate of change and determine if a function is linear from the rate of change.