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)
• Data Set B
• Data Set D
• Data Set A
Data Set C

Answer 1

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

**Data Set A:**
Points: (0, 2), (1, 4), (2, 8), (3, 16), (4, 32), (5, 64)
The y-values double as x-values increase, suggesting an exponential relationship, not linear.

**Data Set B:**
Points: (3, 4), (4, 6), (5, 8), (6, 10), (7, 12)
The y-values increase by 2 for every increase of 1 in x, suggesting a consistent linear relationship, i.e., y = 2x - 2.

**Data Set C:**
Points: (0, 1), (3, 3), (6, 9), (9, 27), (12, 81)
The y-values do not increase in a consistent manner but increase rapidly as x increases, indicating an exponential or polynomial relationship.

**Data Set D:**
Points: (2, 4), (-1, 2), (7, 16), (-4, 32), (1, 64)
The y-values do not follow a consistent pattern with respect to x and are inconsistent, suggesting a nonlinear relationship.

**Conclusion:**
Based on the analysis, **Data Set B** can reasonably be modeled by a linear relationship.