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 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 her claim that the number of pages read (y) is proportional to the number of minutes spent reading (x), Sara would want to demonstrate that there is a consistent ratio between the two variables. This effectively means showing that as the time spent reading increases, the number of pages read increases at a constant rate, resulting in the relationship being linear and passing through the origin.

Among the given options, the best choice to prove her claim is:

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

This option directly demonstrates that there is a linear relationship with a constant ratio, indicating that y is proportional to x. A line through the origin confirms that when x (time spent reading) is zero, y (pages read) is also zero, which is a key characteristic of proportional relationships.

Let's briefly evaluate the other options:

A. By placing the coordinate pairs in a table and showing that they do not create equivalent ratios, Sara would be disproving her claim, which is not her goal.

B. Showing that an equation of the form y = x + c can be written does not necessarily indicate that the relationship is proportional unless c = 0. Without that condition, it wouldn't support her claim.

C. Listing out the coordinate pairs to show that each y-value is a multiple of its associated x-value could be helpful, but it may not be the clearest method compared to plotting it and visually confirming the linearity.

Therefore, option D is the most effective method for Sara to prove her claim.