Question

Use the table to answer the question.

x
(time in seconds) 0 2 4
y
(pages in copy machine) 500 495 490
Interpret the slope in the context of this situation. Give the most simplified rate using whole numbers.

(1 point)
Responses

The slope is 500 pages in the copy machine.
The slope is 500 pages in the copy machine.

The slope is −5
pages every second.
The slope is negative 5 pages every second.

The slope is 2 pages in the copy machine every 5 seconds.
The slope is 2 pages in the copy machine every 5 seconds.

The slope is −5
pages in the copy machine every 2 seconds.

Answer 1

To interpret the slope in the context of the data provided:

The values given show that the number of pages in the copy machine decreases over time. To find the slope, we can calculate it between the points.

Let's calculate the slope between the two points (0, 500) and (2, 495):

- The change in y (number of pages) is:
\( 495 - 500 = -5 \) pages

- The change in x (time) is:
\( 2 - 0 = 2 \) seconds

Now, we can calculate the slope (m) using the formula:

\[
m = \frac{\text{change in } y}{\text{change in } x} = \frac{-5}{2}
\]

So, the slope is \(-\frac{5}{2}\) pages per second, which means that the machine is losing pages at a rate of 5 pages every 2 seconds.

Based on the available responses, the correct interpretation of the slope is:

**The slope is −5 pages in the copy machine every 2 seconds.**