Question

Which of the following methods would help Xavier prove his claim that the number of text messages he sends is proportional to the amount he owes on his monthly phone bill?

Option 1: Xavier could plot data points based on the number of text messages sent in each month and the amount owed to create a straight line on the graph starting at (0.05).
Option 2: Xavier could plot data points based on the number of text messages sent in each month and the amount owed to create a straight line on the graph starting at (0, 0).
Option 3: Xavier could create a table listing the number of text messages sent in each of the months listed and the amount he owed for those months to test for equivalent ratios.
Option 4: Xavier could create equations based on the data collected to prove that as the number of text messages increases, the amount owed also increases.

Answer 1

The best proof for Xavier's proportional claim would be either plotting a straight line on a graph starting at (0, 0), indicating a proportional relationship, or creating a table with equivalent ratios.

Step-by-step explanation:

To prove that Xavier's number of text messages is proportional to the amount he owes on his monthly phone bill, he should choose a method that demonstrates a consistent ratio between the two quantities. Option 1 is incorrect because it suggests a graph starting at (0.05), which does not make sense in this context. Option 2 is the correct approach, as it involves plotting data points to create a straight line on a graph starting at (0, 0), which would indicate a proportional relationship where if there are no text messages sent, no cost is accrued. Option 3 also serves this purpose by creating a table to test for equivalent ratios, which would show proportionality if the ratios are consistent. Option 4 is less direct, as it suggests creating equations based on the data which would show increase but not necessarily proportionality.