1. The problem asks us to identify the types of relationships between variables in four different data sets based on their descriptions and graphs. 2. Important concepts: - A negative linear relationship means as one variable increases, the other decreases. - A perfect linear relationship means all points lie exactly on a straight line. - A strong linear relationship means points lie very close to a straight line. - A nonlinear relationship means the pattern is curved or not a straight line. 3. Analyze each data set: - (a) Top-left graph: Points form a roughly downward sloping straight line, indicating a negative but not perfect linear correlation. - (b) Top-right graph: Points lie exactly on a straight line sloping upwards, indicating a perfect positive linear correlation. - (c) Bottom-left graph: Points lie almost exactly on a straight line sloping downwards, indicating the strongest negative linear correlation. - (d) Bottom-right graph: Points form a curved, nonlinear shape (parabolic or exponential), indicating a strong nonlinear relationship. 4. Final answers: - (a) Top-left graph data set - (b) Top-right graph data set - (c) Bottom-left graph data set - (d) Bottom-right graph data set This matches the descriptions and the data patterns given.