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

Question

(
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.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 read (y) is proportional to the number of minutes spent reading (x), Sara can take the following actions:

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

• This approach demonstrates that for the values of \( y \) and \( x \), the ratios \( \frac{y}{x} \) are constant, which is a characteristic of proportional relationships.

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

• If the points form a straight line through the origin, this indicates that the relationship is proportional, since proportional relationships graph as straight lines that pass through (0, 0).

Therefore, the correct answers are A and D.