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.