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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 C
Data Set C

Data Set B
Data Set B

Data Set D
Data Set D

Data Set A
Data Set A
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1 answer

To determine which data set can reasonably be modeled by a linear relationship, we need to analyze the patterns in the given data sets.

  1. Data Set A:

    • Points: (0, 2), (1, 4), (2, 8), (3, 16), (4, 32), (5, 64)
    • The y-values double as the x-values increase, indicating an exponential growth rather than linear.

  2. Data Set B:

    • Points: (3, 4), (4, 6), (5, 8), (6, 10), (7, 12)
    • The y-values increase consistently by 2 for every increase of 1 in the x-values. This indicates a linear relationship.

  3. Data Set C:

    • Points: (0, 1), (3, 3), (6, 9), (9, 27), (12, 81)
    • The y-values increase rapidly, especially after x = 6 (non-linear increase), indicating a non-linear relationship.

  4. Data Set D:

    • Points: (2, 4), (−1, 2), (7, 16), (−4, 32), (1, 64)
    • This set appears to vary significantly, and the y-values do not show a consistent rate of change as the x-values change, indicating a non-linear relationship.

Conclusion: The only data set that can reasonably be modeled by a linear relationship is Data Set B.

Answer: Data Set B