https://file.aiquickdraw.com/mathbot/file/1730560352567moatj391.jpg

To answer the questions in the image, let's analyze each scatter plot in terms of the relationships it shows.

### Question (a): Strongest Positive Linear Relationship

The strongest positive linear relationship is characterized by data points that form a straight, upward-sloping line. This indicates a strong positive correlation between the two variables.

- **Figure 3** shows a perfect upward line, meaning there is a strong positive linear relationship between \( w \) and \( t \).
- In contrast, Figures 1, 2, and 4 show either weaker positive, negative, or non-linear relationships.

**Answer for (a):** **Figure 3**

### Question (b): Perfect Negative Linear Relationship

A perfect negative linear relationship would have data points forming a straight, downward-sloping line.

- Among the figures, **Figure 2** shows a clear downward trend with data points nearly aligned, indicating a strong negative linear relationship between \( u \) and \( v \).
- None of the other figures show a similar trend.

**Answer for (b):** **Figure 2**

Let me know if you want more detailed explanations on linear relationships or have other questions.

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Here are some additional questions to consider:
1. What is the difference between positive and negative linear relationships?
2. How can we quantify the strength of a linear relationship?
3. Why is Figure 4 not suitable for questions (a) and (b)?
4. How could we calculate correlation coefficients for these data sets?
5. What methods can we use to confirm a perfect linear relationship?

**Tip:** In scatter plots, look for alignment of points to determine the strength and direction of the linear relationship.

Which data set indicates the strongest positive linear relationship between two variables? Which data set indicates a perfect negative linear relationship between its two variables?

Learn how to identify the strongest positive and perfect negative linear relationships between variables using scatter plots. This solution explains the identification of linear relationships and correlation concepts with examples, suitable for high school students studying statistics.

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