Blog 4 Miles VB

Miles Van Blarcum

Blog 4- Rate of Change

Hello class! My name is Professor Van Blarcum. Today we will be going over an interesting and important topic: rate of change. Now- from real life and your previous math experience, you probably know what rate of change is. Simply put, rate of change is the measure or steepness of a straight line. Essentially the same as the slope of a line. More simply put, the rate of change is a rate of how one quantity changes in comparison to another quantity.

So where is this seen? Well, most commonly it is used in lines and graphs. In a graph, the Rate of Change is found by dividing the vertical change by the horizontal change. In other words, it is the change in Y over the change in X. 

In the image below, a roofer can find the slope/rate of change by comparing the height of the roof (Y) to the width of the roof (X). A little example to go with this image comes from regentsprep.org. It says, "The building code for using asphalt shingles on roofs states that the minimum pitch must be a rise of 4" for every 12" of horizontal distance (run) covered.  Asphalt shingles are not to be used on roofs that have very little steepness.  Builders check to see if the pitch (slope) of the roof is  before using asphalt shingles." 

The rate of change in a situation can be negative. This would be when the starting Y point is greater than the ending Y point. For instance, the image to the left would have a negative rate of change if you drew a line between the apex of the roof line to the right gutter side of the line. This is because the Y value decreases between the apex and the lower point near the gutter.

Heres a clearer example of a positive Rate of Change: 

And heres a clearer example of a negative Rate of Change:

Simple right? Well there can also be a Zero rate of change, and this is when the line has no slope and does not increase or decrease. Easy stuff. 

Lets do a problem. Find the Rate of Change of the table below. 

First, remember that the ROC = Change in Y / Change in X. So in this case, that means Distance/time.

Know it? It would be (160-80)/(4-2), which translates to 80/2. This means the Rate of Change is equal to 40 miles per hour. 

This is another real world application of the rate of change. It is a relatively simple concept, but is important in countless mathematic applications.