Use the data sets to answer the question.

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 A
Data Set A

Data Set D

Answer 1

To determine which data set can reasonably be modeled by a linear relationship, we should first analyze the nature of each data set based on its coordinates:

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

   • The y-values are increasing rapidly, suggesting an exponential or quadratic relationship.

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

   • The y-values increase by a constant rate (2), indicating a linear relationship. This looks linear.

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

   • Although there is some increase, especially between (9,27) and (12,81), it appears more exponential due to the drastic increase in y-values.

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

   • The y-values do not show a linear trend as they vary non-uniformly.

Based on this analysis, Data Set B is the only one that can be reasonably modeled by a linear relationship, as it shows a consistent increase in y-values corresponding to a consistent increase in x-values.

Thus, the answer is: Data Set B