1. The problem asks to identify which scatter diagrams correspond to the strongest positive and negative linear correlations between variables $x$ and $y$. 2. Recall that a positive linear correlation means as $x$ increases, $y$ also increases, and a negative linear correlation means as $x$ increases, $y$ decreases. 3. For strongest positive linear correlation, we look for the graph where points lie closest to a straight line with positive slope. 4. For strongest negative linear correlation, we look for the graph where points lie closest to a straight line with negative slope. 5. From the descriptions: - Graph (a) shows a positive linear trend in the first quadrant. - Graph (b) also shows a positive linear trend but starting from a lower $y$ value. - Graph (c) shows a negative linear trend. - Graph (d) shows a negative linear trend but more spread out than (c). 6. Since (a) and (b) both have positive trends, the strongest positive correlation is graph (a) because it is described first and presumably less spread out. 7. Between (c) and (d), both have negative trends, but (c) is less spread out, indicating a stronger negative correlation. Final answers: - (a) strongest positive linear correlation: graph (a) - (b) strongest negative linear correlation: graph (c)