Question

Sara claims that the number of pages she has read in her book is proportional to the number of minutes that she has spent reading. She collects several data points to prove her claim and expresses the data points as
(
x
,
y
)
coordinate pairs.

Which of the following actions could Sara take to prove her claim? Select two that apply.
A.
Place the coordinate pairs in a table and show that they create equivalent ratios.

B.
Use the coordinate pairs to show that an equation of the form y = x + c can be written.

C.
List out the coordinate pairs and show that each y-value is a multiple of its associated x-value.

D.
Plot the coordinate pairs on a graph and show that the points make a straight line through the origin.

Answer 1

To prove that the number of pages Sara has read (y) is proportional to the number of minutes she has spent reading (x), she can take the following actions:

**A. Place the coordinate pairs in a table and show that they create equivalent ratios.**

This option demonstrates that the ratio of pages read to minutes spent is consistent across all data points, confirming proportionality.

**D. Plot the coordinate pairs on a graph and show that the points make a straight line through the origin.**

This option visually shows that there is a linear relationship between pages read and minutes spent, which would indicate that they are proportional. A line through the origin signifies that when no time is spent reading (x = 0), no pages are read (y = 0), consistent with the definition of proportionality.

Therefore, the correct actions are **A** and **D**.