Question

Question

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 C
Data Set C

Data Set B
Data Set B

Data Set D

Answer 1

To determine which data set can be reasonably modeled by a linear relationship, we should analyze the points given in each data set:

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

• This set shows an exponential growth pattern (each y-value doubles as x increases by 1).

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

• This set appears to show a consistent linear increase (the y-values increase by 2 as x increases by 1).

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

• This set also shows exponential growth, especially in the later points, indicating that it is not linear.

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

• This set does not appear to follow a linear pattern, as the y-values increase inconsistently with x.

Conclusion

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

So the correct response is: Data Set B