https://file.aiquickdraw.com/mathbot/file/1727404172253ee46f8it.jpg

The table provides the weights (in pounds) and highway mileage (in miles per gallon) for seven automobiles:

| Weight (lb) | 3055 | 3165 | 3700 | 3985 | 4345 | 2665 | 3370 |
|-------------|------|------|------|------|------|------|------|
| Highway (mpg) | 33 | 32 | 27 | 24 | 23 | 36 | 30 |

### First Task: Identifying the Correct Scatterplot
We need to match the data from the table with the scatterplots shown in the image to determine which one accurately represents the relationship between weight and highway mileage.

- The data shows that as weight increases, highway mileage generally decreases. Therefore, the scatterplot should depict a downward trend.

#### Option Analysis:
- **Option A**: Displays a general downward trend where highway mileage decreases as weight increases. This matches the data pattern.
- **Option B**: Shows an increasing trend, which contradicts the data.
- **Option C**: The points don't follow the same downward trend.
- **Option D**: Shows an upward trend, which contradicts the data.

Thus, **Option A** is the correct scatterplot.

### Second Task: Determining the Linear Relationship
From the scatterplot (and table data), we observe a clear downward trend. This suggests a negative correlation: as weight increases, highway mileage decreases.

- This fits the description in **Option B**: "Yes, as the weight increases the highway mileage decreases."

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Would you like a detailed explanation on scatterplots or correlation? Let me know if you have any further questions.

Here are 5 related questions:
1. What is the difference between positive and negative correlation in scatterplots?
2. How do we determine if a relationship is linear or nonlinear?
3. What does it mean if a scatterplot shows no correlation?
4. How can we calculate the correlation coefficient from data?
5. What types of real-world data might show similar trends?

**Tip**: Always look at the overall trend of the scatterplot to identify the type of correlation (if any).

Based on the scatterplot and table of weights and highway mileage amounts for seven automobiles, determine which scatterplot best represents the data and whether there is a linear relationship between weight and highway mileage.

Learn how to interpret scatterplots using weight (lb) and highway mileage (mpg) data. This problem explores how increasing weight can lead to decreased highway mileage, showing a negative linear correlation. Suitable for students in Grades 8-12.

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