Question

Interpret the slope in the context of this situation. Give the most simplified rate using whole numbers.

(0,5) (5,8)

A. Someone had 5 weeks to read a book.
B. Someone is reading 5 books every 3 weeks
C. Someone read 5 books in a week.
D. Someone reads 3 books every 5 weeks.

Answer 1

To find the slope between the points (0, 5) and (5, 8), we calculate the change in the y-coordinates divided by the change in the x-coordinates.

The slope \( m \) is calculated as follows:

1. Identify the coordinates:
- Point 1: (0, 5), where 0 is the x-value (weeks) and 5 is the y-value (books).
- Point 2: (5, 8), where 5 is the x-value (weeks) and 8 is the y-value (books).

2. Calculate the change in y (books read) and change in x (weeks):
- Change in y: \( 8 - 5 = 3 \)
- Change in x: \( 5 - 0 = 5 \)

3. Calculate the slope:
\[
m = \frac{\text{Change in y}}{\text{Change in x}} = \frac{3}{5}
\]

This means that for every 5 weeks, the person reads 3 more books.

Now, we can interpret the slope in the context of the given options:

A. Someone had 5 weeks to read a book. (This option doesn't fit with our slope interpretation.)

B. Someone is reading 5 books every 3 weeks. (This option suggests a different relationship.)

C. Someone read 5 books in a week. (This option does not match our slope.)

D. Someone reads 3 books every 5 weeks. (This option aligns with our slope interpretation, indicating a reading rate of 3 books for every 5 weeks.)

Therefore, the correct choice is:

**D. Someone reads 3 books every 5 weeks.**