To determine which data set can be modeled by a linear relationship, we will analyze the patterns and trends of each data set based on the provided coordinates.
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Data Set A:
- Points: (0,2), (1,4), (2,8), (3,16), (4,32), (5,64)
- Observations: The y-values double as the x-values increase, indicating an exponential growth rather than a linear relationship.
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Data Set B:
- Points: (3,4), (4,6), (5,8), (6,10), (7,12)
- Observations: The y-values increase by 2 for each increase of 1 in the x-values, which suggests a linear relationship (can be represented by the equation \(y = 2x - 2\)).
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Data Set C:
- Points: (0,1), (3,3), (6,9), (9,27), (12,81)
- Observations: The y-values increase at an increasing rate, indicating a possible exponential relationship rather than linear.
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Data Set D:
- Points: (2,4), (−1,2), (7,16), (−4,32), (1,64)
- Observations: The y-values do not follow a consistent increase or rate of change as x fluctuates. This suggests that this data set does not have a linear relationship.
Based on this analysis, the only data set that appears to be reasonably modeled by a linear relationship is Data Set B.
Final Answer: Data Set B