The question asks for the meaning of the rate of change in the graph. To solve this, let us determine the slope (rate of change) based on the provided data points.

Step 1: Extract key data points

From the graph:

• Point 1: $(0, 30)$
• Point 2: $(8, 62)$

Step 2: Calculate the slope (rate of change)

The formula for slope is: $m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the values: $m = \frac{62 - 30}{8 - 0} = \frac{32}{8} = 4$

Thus, the rate of change is $4$, meaning the number of catfish increases by 4 per month.

Step 3: Identify the correct answer

The correct interpretation of the rate of change is:

D. It means the number of catfish increased at a rate of 4 catfish per month.

Let me know if you'd like further clarification or have any additional questions! Here are some related questions for practice:

Practice Questions

1. How would the slope change if the final point were $(8, 70)$ instead of $(8, 62)$?
2. What does the y-intercept ($30$) represent in the context of this problem?
3. If the study continued to 12 months, how many catfish would be expected in the lake?
4. How is the slope of a graph related to real-world rates of change?
5. Can you think of other scenarios where a similar rate of change might be observed?

Tip

When interpreting graphs, always identify the slope and y-intercept first, as they often reveal important real-world meanings.