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

A and D.

Reason: A shows the ratio y/x is constant (y = kx), and D shows the points lie on a line through the origin (graph of y = kx). B is wrong because y = x + c is not proportional unless c = 0. C is ambiguous (saying "multiple" often implies integer multiples); the correct condition is that each y is a constant scalar times x, which is what A and D demonstrate.