To determine which scatterplot shows a linear association, we need to analyze the relationship between the values of \( x \) and \( y \) in each table.
-
First Set:
- \( x = [5, 8, 2, 4, 6, 12, 10, 1, 3, 7] \)
- \( y = [550, 800, 350, 450, 700, 1000, 900, 250, 400, 750] \)
- Observation: The values of \( y \) do not consistently increase or decrease as \( x \) changes. This does not exhibit a linear relationship.
-
Second Set:
- \( x = [5, 8, 2, 4, 6, 12, 10, 1, 3, 7] \)
- \( y = [800, 700, 350, 450, 500, 1000, 900, 250, 400, 750] \)
- Observation: Similar to the first set, \( y \) values also do not consistently increase or decrease with changes in \( x \).
-
Third Set:
- \( x = [5, 8, 2, 4, 6, 12, 10, 1, 3, 7] \)
- \( y = [550, 800, 250, 500, 500, 400, 650, 150, 400, 750] \)
- Observation: There is no clear linear correlation as the \( y \) values fluctuate without a clear upward or downward pattern.
-
Fourth Set:
- \( x = [5, 8, 2, 4, 6, 12, 10, 1, 3, 7] \)
- \( y = [550, 800, 250, 300, 700, 1000, 650, 300, 100, 700] \)
- Observation: Although there are some increases and decreases, overall fluctuations in \( y \) values do not suggest a linear relationship.
Conclusion:
From the analysis, none of the scatterplots appear to show a clear linear association between \( x \) and \( y \). If you must choose one based on minimal fluctuations closest to a linear relationship, it would be wise to look for the dataset where the values of \( y \) are more consistently trending upward or downward as \( x \) changes. However, please provide additional context or criteria if you have specific details in mind to evaluate more effectively. If there was a mistake or a specific scatterplot was indicated based on previous observations, it is representative to choose that based on best fit rather than definitive linearity.