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 B
Data Set B

Data Set D
Data Set D

Data Set C

Answer 1

To determine which data set can be modeled by a linear relationship, we will analyze the patterns and trends of each data set based on the provided coordinates.

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

2. **Data Set B:**
- Points: (3,4), (4,6), (5,8), (6,10), (7,12)
- Observations: The y-values increase by 2 for each increase of 1 in the x-values, which suggests a linear relationship (can be represented by the equation \(y = 2x - 2\)).

3. **Data Set C:**
- Points: (0,1), (3,3), (6,9), (9,27), (12,81)
- Observations: The y-values increase at an increasing rate, indicating a possible exponential relationship rather than linear.

4. **Data Set D:**
- Points: (2,4), (−1,2), (7,16), (−4,32), (1,64)
- Observations: The y-values do not follow a consistent increase or rate of change as x fluctuates. This suggests that this data set does not have a linear relationship.

Based on this analysis, the only data set that appears to be reasonably modeled by a linear relationship is **Data Set B**.

**Final Answer: Data Set B**