 Now, since all we need to find the change or a rate of change is the values of the endpoints, we can also find this from a graph or a function. So for example, suppose an airline goes on a six-hour flight. The graph shows the height of the airplane in kilometers, t hours after it takes off. And let's find the average rate of change between the time it takes off and three hours into the flight and the average rate of change during the last hour of the flight. So we need to know where it was. It took off at t equals zero and three hours into the flight is at t equals three. And we see that at t equals zero, the plane's altitude was zero kilometers. And at t equals three, the plane's altitude was 12 kilometers. And so the rate of change is the change in quantity divided by how long the change took. Remember the change in quantity is the ending amount minus the starting amount. We ended at 12 kilometers and we started at zero kilometers. That change took three hours. And so our rate of change, 12 kilometers divided by three hours or four kilometers per hour. How about during the last hour of flight? Since the flight was six hours, the last hour of flight is the time between t equals five and t equals six hours after the plane takes off. And so we want to know the plane's height at t equals five and the plane's height at t equals six. And these are four kilometers and two kilometers. So again our rate of change is the change in quantity divided by how long the change took. The change is the ending amount minus the starting amount. And we ended at a height of two kilometers. We started at a height of four kilometers. So that gives us our difference. Minus two kilometers and the change took one hour. And so our rate of change is minus two kilometers per hour. And again, as with change amounts, we should always choose one. Either include the sign or omit the sign and include a direction. And so we might say that during the first three hours, the plane's height changed by plus three kilometers per hour. Now since this is positive, we could omit the plus sign and just say three kilometers per hour. During the last hour, the plane's height changed by minus two kilometers per hour. Or during the last hour, the plane's height decreased by two kilometers per hour, where since we used the word decreased, we omit the sign.