Question

The graph represents the linear relationship between the number of books Layla has read and the number of months she has been a member of a book club.
(4,6)
(2,3)
Which of these statements is supported by the rate of change in this relationship
A. Layla read 2 books in the first 3 months she was a member of the book club.
B. Layla read 3 books in the first 2 months she was a member of the book club
C. Layla read 3 books in the first 4 months she was a member of the book club
D. Layla read 4 books in the first 3 months she was a member of the book club.

Answer 1

To determine which statement is supported by the rate of change represented by the graph, we first need to calculate the slope (rate of change) between the two points given: (2, 3) and (4, 6).

The slope (m) can be calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (2, 3) \((x_1, y_1)\) and (4, 6) \((x_2, y_2)\):

\[
m = \frac{6 - 3}{4 - 2} = \frac{3}{2} = 1.5
\]

The slope of 1.5 indicates that Layla reads 1.5 books per month.

Now let's analyze each statement:

A. Layla read 2 books in the first 3 months she was a member of the book club.
- If Layla reads 1.5 books/month, in 3 months, she would read \(1.5 \times 3 = 4.5\) books (not 2). This statement is not supported.

B. Layla read 3 books in the first 2 months she was a member of the book club.
- In 2 months, she would read \(1.5 \times 2 = 3\) books. This statement is supported.

C. Layla read 3 books in the first 4 months she was a member of the book club.
- In 4 months, she would read \(1.5 \times 4 = 6\) books (not 3). This statement is not supported.

D. Layla read 4 books in the first 3 months she was a member of the book club.
- In 3 months, she would read \(1.5 \times 3 = 4.5\) books (not 4). This statement is not supported.

Thus, only statement **B** is supported by the rate of change in this relationship.