https://file.aiquickdraw.com/mathbot/file/17297764702097o2ctnpl.jpg

The problem in the image asks about the rate of change for a line representing the growth of catfish over time, measured in months. To interpret this graph and answer the question, let's analyze the details.

The graph shows:
- The x-axis represents the number of months.
- The y-axis represents the number of catfish.
- The line rises from 30 catfish at month 0 to 62 catfish at month 8.

### Calculating the rate of change:
- The number of catfish increased from 30 to 62, so the total change in catfish is \( 62 - 30 = 32 \) catfish.
- The change in time is 8 months.

The rate of change is:
\[
\text{Rate of change} = \frac{\text{Change in catfish}}{\text{Change in time}} = \frac{32}{8} = 4 \text{ catfish per month}.
\]

### Conclusion:
The rate of change indicates that the number of catfish increased at a rate of 4 catfish per month, which matches option D.

Would you like further clarification on any part of this explanation?

Here are 5 related questions to explore:
1. How do you calculate the slope from a graph of a line?
2. What does a steeper slope on a graph represent in real-world terms?
3. How would the graph look if the rate of change were negative?
4. How can we use the y-intercept to understand initial conditions in this context?
5. What happens to the graph if the growth rate doubles?

**Tip:** The rate of change, also known as the slope, is crucial for understanding how fast one quantity changes relative to another.

What is the meaning of the rate of change for the line in the graph?

Learn how to calculate the rate of change from a graph showing the growth of catfish over time. This problem explains how to interpret the slope and find the rate of increase in the population of catfish. Suitable for students in Grades 6-8.

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