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To solve this problem, we will calculate the average rate of change in the number of books per year in the library from 1992 to 1998. 

The formula for the average rate of change is:

\[
\text{Average rate of change} = \frac{\text{Change in books}}{\text{Change in years}} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Where:
- \( y_2 = 16,000 \) (number of books in 1998),
- \( y_1 = 19,000 \) (number of books in 1992),
- \( x_2 = 1998 \),
- \( x_1 = 1992 \).

Let's calculate:

\[
\text{Change in books} = 16,000 - 19,000 = -3,000
\]
\[
\text{Change in years} = 1998 - 1992 = 6
\]
\[
\text{Average rate of change} = \frac{-3,000}{6} = -500 \text{ books per year}
\]

### Answers:
- **Increase or Decrease?** Decrease (since the rate of change is negative).
- **Average Rate of Change?** -500 books per year.

Would you like more details on this or any specific part of the process? 

Here are 5 related questions:
1. What is the significance of a negative rate of change in this context?
2. How can we interpret the slope in the context of a decreasing library collection?
3. If the rate of change continued, how many books would the library have in 2002?
4. What would the average rate of change be if the number of books increased from 16,000 in 1998 to 18,000 in 2004?
5. How does the concept of average rate of change relate to linear functions?

**Tip**: The average rate of change formula is very similar to the slope formula used for lines in coordinate geometry!

In 1998, a public library had 16,000 books. In 1992, the library had 19,000 books. What is the average rate of change in number of books per year?

This problem involves calculating the average rate of change in the number of books in a public library from 1992 to 1998. In 1992, the library had 19,000 books, and by 1998, the number dropped to 16,000. The average rate of change is found using the formula for rate of change, with a result of -500 books per year, indicating a decrease.

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