` (##KPL_SAT_PRD_PLS_C09_E01_001_Q01.png" width="80%">
The scatterplot shows the prevalence of obesity plotted against the prevalence of diabetes in various ares of the United States. Which of the following best estimates the average rate of change in the prevalence of diabetes as comared to the prevalence of obesity ?

Options

A. `0.3`
B. `0.9`
C. `1.1`
D. 3

Explanation

To solve the problem of estimating the average rate of change in the prevalence of diabetes compared to the prevalence of obesity using the scatterplot, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Variables**:
- The x-axis represents the prevalence of obesity.
- The y-axis represents the prevalence of diabetes.

2. **Select Points on the Scatterplot**:
- Choose two points on the line of best fit from the scatterplot. For this example, let's select:
- Point A: (20, 9)
- Point B: (30, 11)

3. **Write Down the Coordinates**:
- The coordinates of the two points are:
- Point A: (20, 9)
- Point B: (30, 11)

4. **Calculate the Change in y (Δy)**:
- Δy = y2 - y1 = 11 - 9 = 2

5. **Calculate the Change in x (Δx)**:
- Δx = x2 - x1 = 30 - 20 = 10

6. **Calculate the Slope (Average Rate of Change)**:
- The slope (m) is given by the formula:
\[ m = \frac{Δy}{Δx} = \frac{2}{10} = 0.2 \]

7. **Estimate the Average Rate of Change**:
- The average rate of change in the prevalence of diabetes compared to the prevalence of obesity is approximately 0.2.

8. **Select the Nearest Answer**:
- According to the options provided in the question, the nearest answer to 0.2 is 0.3.

### Final Answer:
The best estimate for the average rate of change in the prevalence of diabetes compared to the prevalence of obesity is **0.3**.

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