To determine which data set can reasonably be modeled by a linear relationship, we first need to consider the nature of the data points for each set.
Data Set A:
Points: (0,2), (1,4), (2,8), (3,16), (4,32), (5,64)
- This set appears to increase exponentially. As the x-values increase, the y-values increase much faster, indicating a nonlinear relationship.
Data Set B:
Points: (3,4), (4,6), (5,8), (6,10), (7,12)
- This set is characterized by consistent increments. The y-values increase by 2 for every increment of 1 in the x-values, suggesting a linear relationship.
Data Set C:
Points: (0,1), (3,3), (6,9), (9,27), (12,81)
- The y-values do not increase at a constant rate. This appears to have a nonlinear pattern, particularly with the last few points increasing rapidly.
Data Set D:
Points: (2,4), (−1,2), (7,16), (−4,32), (1,64)
- The relationship is irregular and does not show a clear linear trend, indicating a nonlinear relationship.
Based on the analysis, Data Set B is the only data set that can reasonably be modeled by a linear relationship.
Conclusion:
The correct response is Data Set B.