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.

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.