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Use the data sets to answer the question.

Data Set A: (0,2)
, (1,4)
, (2,8)
, (3,16)
, (4,32)
, (5,64)


Data Set B: (3,4)
, (4,6)
, (5,8)
, (6,10)
, (7,12)


Data Set C: (0,1)
, (3,3)
, (6,9)
, (9,27)
, (12,81)


Data Set D: (2,4)
, (−1,2)
, (7,16)
, (−4,32)
, (1,64)


Create a scatterplot for each of the data sets shown. Which data set can reasonably be modeled by a linear relationship?

(1 point)
Responses

Data Set D
Data Set D

Data Set B
Data Set B

Data Set A
Data Set A

Data Set C
Data Set C
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1 answer

To determine which data set can reasonably be modeled by a linear relationship, we need to consider the scatterplots of each data set.

Data Set A:

  • Points: (0,2), (1,4), (2,8), (3,16), (4,32), (5,64)
  • This data set exhibits exponential growth; each y-value is a power of 2 (e.g., 2, 4, 8, 16, 32, 64). Therefore, it is not linear.

Data Set B:

  • Points: (3,4), (4,6), (5,8), (6,10), (7,12)
  • The y-values increase consistently by 2 for each increment of 1 in x. This suggests a linear relationship (y = 2x - 2), as the change in y is constant.

Data Set C:

  • Points: (0,1), (3,3), (6,9), (9,27), (12,81)
  • The y-values increase rapidly and are not consistent; they show an exponential pattern. Thus, this data set does not exhibit a linear relationship.

Data Set D:

  • Points: (2,4), (−1,2), (7,16), (−4,32), (1,64)
  • The points seem scattered without a consistent pattern, and the y-values do not change at a constant rate with x. Hence, this data set does not demonstrate a linear relationship.

Conclusion:

Among the data sets, Data Set B is the only one that can reasonably be modeled by a linear relationship because the increase in y-values is consistent with a linear trend.

Final Answer: Data Set B