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?

A.
Place the coordinate pairs in a table and show that they do not create equivalent ratios.

B.
Use the coordinate pairs to show that an equation of the form
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 is proportional to the number of minutes she has spent reading, she needs to demonstrate that the relationship between the two quantities is constant, meaning that as one increases, the other increases at a constant ratio.

Among the options provided, the most effective actions she could take are:

**C. List out the coordinate pairs and show that each y-value is a multiple of its associated x-value.**
- This action would clearly demonstrate proportionality, as it shows that there is a consistent ratio between the pages read (y) and the time spent reading (x).

**D. Plot the coordinate pairs on a graph and show that the points make a straight line through the origin.**
- This is also a strong demonstration of proportionality, as a straight line that passes through the origin indicates that there is a constant ratio between the two variables.

Both C and D are valid and effective to prove her claim. However, if you had to choose one action primarily, then D would be the clearest demonstration of the proportionality because it visually conveys the relationship.

Thus, the best answers are **C** and **D**. If only one choice must be made for proving her claim, then **D** is the most definitive.