Rate of Change in Graphs In this lesson let’s learn about the rate of change when it comes to graphs. We’ll do two problems. Let’s do the first one first. It says do the graphs depict a constant rate of change or a variable rate of change. We’re given two graphs, this is graph A and this is graph B. So in order to do this, we really have to use only one principle. The key tip to remember is if the graph is a straight line. If the graph is a straight line then the rate of change is constant. If not it’s a variable, so let’s look at graph A. Well the line is not a straight line which means this is a variable rate of change. Here it is a straight line so it’s constant, quite simple. Now let’s look at the second problem, it says the graph shows the distance a bicyclist travels over time. As we can see we’ve got the north, south which is the Y axis has the distance in miles and the X axis is time and hours. The question says does the bicyclist travel at a constant or a variable speed. Let’s do that first and we also have to find how fast is he or she going. So constant or variable, well is the line straight or is it not? Well it’s a straight line which means the rate of change is constant. Rate of change is constant, so the bicyclist travels at constant speed. They don’t go up or down as far as the speed goes. Now let’s look at how fast is the bicycle is going. Well the speed of the bicyclist is in fact the slope of the line. Slope is rise over a run. Rise is, let’s pick two points on the graph. Let’s pick this point and this point. What is the rise, well I’ve gone from here to here and the number of units I’ve gone up is 20 to 40 which means the slope rise is 20. The run, how many units have I gone left or right, well it looks like I’ve started at 1 ½ and I went to 2 ½. So I went one unit, so the rise is 20, the run is unit, so run is 1. So the slope is 20/1 or the slope equals 20. Now the unit of measurement here, distance is in miles times in hours. So the speed of the bicyclist equals 20miles per hour, that’s what we were looking for.