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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 A
Data Set A

Data Set B
Data Set B

Data Set D
Data Set D

Data Set C

1 answer

To determine which data set can be reasonably modeled by a linear relationship, let's summarize the given data sets:

  1. Data Set A:

    • Points: (0, 2), (1, 4), (2, 8), (3, 16), (4, 32), (5, 64)
    • This set shows exponential growth as y-values double each time x increases by 1.

  2. Data Set B:

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

  3. Data Set C:

    • Points: (0, 1), (3, 3), (6, 9), (9, 27), (12, 81)
    • The y-values do not follow a linear pattern and seem to reflect exponential growth as they increase rapidly.

  4. Data Set D:

    • Points: (2, 4), (−1, 2), (7, 16), (−4, 32), (1, 64)
    • The pattern does not appear linear; the y-values vary significantly and do not follow a consistent rate of change.

Conclusion: Only Data Set B can be reasonably modeled by a linear relationship, as the change in y for a consistent change in x is constant.

Therefore, the answer is: Data Set B