1. **Problem Statement:** We are asked to identify which data sets correspond to specific values or characteristics of the sample correlation coefficient $r$ based on the descriptions of four graphs and their data. 2. **Recall the definition of $r$:** The sample correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. It ranges from $-1$ to $1$. - $r = -1$ means a perfect negative linear relationship. - $r$ close to $0$ means no linear relationship. - Negative $r$ values indicate a negative (downward) trend. 3. **Analyze each graph and data set:** - **Figure 1 (Top-left):** Points decrease perfectly along a straight line from top-left to bottom-right, so $r = -1$. - **Figure 2 (Top-right):** Points show a strong but not perfect negative linear trend. - **Figure 3 (Bottom-left):** Points scattered randomly, no trend, so $r$ close to $0$. - **Figure 4 (Bottom-right):** Points show a negative but imperfect linear relationship. 4. **Match the data sets to the graphs:** - Data set with $u,v$ decreases perfectly from (1,10) to (10,1) matching Figure 1, so $r = -1$. - Data set with $x,y$ shows increasing trend, so not negative. - Data set with $w,t$ is scattered, no clear trend, so $r$ close to $0$. - Data set with $m,n$ shows a general downward trend but not perfect, so negative but imperfect. 5. **Answer each question:** (a) $r = -1$ corresponds to the data set $(u,v)$ (Figure 1). (b) Strongest negative linear relationship is also $(u,v)$ (Figure 1) since $r = -1$ is the strongest possible negative correlation. (c) $r$ closest to $0$ corresponds to $(w,t)$ (Figure 3) with scattered points. (d) Negative but not perfect linear relationship corresponds to $(m,n)$ (Figure 4). **Final answers:** (a) $(u,v)$ (b) $(u,v)$ (c) $(w,t)$ (d) $(m,n)$