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, let's analyze each of the provided data sets.

1. Data Set A:

   • Points: (0,2), (1,4), (2,8), (3,16), (4,32), (5,64)
   • This data represents exponential growth. The y-values double as the x-values increase. Therefore, it does not have a linear relationship.

2. Data Set B:

   • Points: (3,4), (4,6), (5,8), (6,10), (7,12)
   • This data shows a constant increase in y as x increases, specifically the y-values increase by 2 for every increase of 1 in x. This can be represented by a linear equation (y = 2x + 2). Therefore, this data set can reasonably be modeled by a linear relationship.

3. Data Set C:

   • Points: (0,1), (3,3), (6,9), (9,27), (12,81)
   • This data appears to show more of a polynomial or exponential curve than a straight line, especially due to the rapid increase seen with the final points. Therefore, it does not display a linear relationship.

4. Data Set D:

   • Points: (2,4), (−1,2), (7,16), (−4,32), (1,64)
   • The values are varied and do not follow a consistent pattern suitable for a linear relationship. The changes in y with respect to x are not uniform.

Based on this analysis:

Response: Data Set B can reasonably be modeled by a linear relationship.