Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed
3 per book he borrows. Here’s a graph that shows a system of equations for this scenario where 2 is the number of books Aaden borrows and y is the total cost of the subscription: y (cost) 150 96 100 50 0 * (books) 0 10 20 30 40 50 60 What does point R represent in this context? (books) 20 40 What does point R represent in this context? Choose 1 answer: A number of books and their cost where the subscription with the annual fee costs less INCORRECT A number of books and their cost where the subscription that charges per book costs less Point R is on both Line A and Line B, so neither cost is higher for the number of books represented by the x-coordinate of R A number of books and their cost where both subscriptions cost the same A number of books and their cost that is not possible with either subscription Stuck? Watch a video or use a hint; Report a problem 3/4 Help center FAQ
The Correct Answer and Explanation is:
Based on the provided image and the principles of interpreting systems of linear equations, the correct answer is:
C) A number of books and their cost where both subscriptions cost the same.
Explanation:
In mathematics, a graph can be used to visualize the relationship between two or more variables. In this scenario, we have a system of two linear equations, represented by two straight lines on the graph. Let’s break down what each part of the graph represents to understand the meaning of point R.
- The Axes: The horizontal axis, or x-axis, represents the number of books Aaden borrows. The vertical axis, or y-axis, represents the total cost of the subscription.
- The Lines: Each of the two intersecting purple lines represents one of the two subscription options. A point (x, y) on a specific line tells you the total cost (y) for borrowing a certain number of books (x) under that particular plan. For example, one line might represent a plan with a high annual fee but a low cost per book, while the other might have no annual fee but a higher cost per book.
- The Intersection Point (R): Point R is the unique location where the two lines cross each other. In a system of equations, the intersection point is the solution that satisfies both equations simultaneously. This means that the x-coordinate and y-coordinate of point R are valid for both subscription plans.
In the context of this problem, the x-coordinate of point R is the specific number of books for which the total cost (the y-coordinate of R) is exactly the same for both subscription plans. This point is often referred to as the “break-even point.” If Aaden borrows fewer books than the number at point R, one plan will be cheaper. If he borrows more books, the other plan will become the better deal. However, at the exact number of books represented by point R, there is no difference in cost between the two subscriptions.
Therefore, point R represents the precise number of books and the corresponding cost at which both subscription options cost the exact same amount.
