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To solve the average rate of change from the graph, we will use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{\text{Change in number of trips}}{\text{Change in time}}
\]

We are asked to calculate the rate of change for three different intervals:

1. **From 1992 to 1995**:
   - In 1992, the number of trips is 8.5 million.
   - In 1995, the number of trips is 7.5 million.
   \[
   \text{Rate of change} = \frac{7.5 - 8.5}{1995 - 1992} = \frac{-1.0}{3} = -0.333 \text{ million trips per year.}
   \]

2. **From 1995 to 2000**:
   - In 1995, the number of trips is 7.5 million.
   - In 2000, the number of trips is 9.3 million.
   \[
   \text{Rate of change} = \frac{9.3 - 7.5}{2000 - 1995} = \frac{1.8}{5} = 0.360 \text{ million trips per year.}
   \]

3. **From 1992 to 1998**:
   - In 1992, the number of trips is 8.5 million.
   - In 1998, the number of trips is 8.6 million.
   \[
   \text{Rate of change} = \frac{8.6 - 8.5}{1998 - 1992} = \frac{0.1}{6} = 0.017 \text{ million trips per year.}
   \]

Let me know if you'd like more details or have any questions. 

Here are five related questions to deepen your understanding:
1. How is the average rate of change different from the instantaneous rate of change?
2. What does the negative rate of change from 1992 to 1995 indicate about the number of trips?
3. Why is the rate of change different in each interval?
4. How would the rate of change differ if calculated for shorter periods?
5. How is the slope of a graph related to the average rate of change?

**Tip:** The average rate of change is equivalent to the slope of the secant line between two points on a graph.

The graph shows the number of trips taken annually on a certain state's mass transportation system. Find the average rate of change of the number of trips from 1992 to 1995, from 1995 to 2000, and from 1992 to 1998.

This problem demonstrates how to calculate the average rate of change in the number of trips from 1992 to 2000 for a state's mass transportation system. Using the formula for the average rate of change, we explore different intervals between 1992 and 1998. Suitable for Grades 8-10.

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