Question

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

The slope is −5
pages in the copy machine every 2 seconds.
The slope is negative 5 pages in the copy machine every 2 seconds.
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Answer 1

To find the slope (rate of change) from the given data, we can use the formula for the slope between two points:

\[
\text{slope} = \frac{\Delta y}{\Delta x}
\]

Here, \(\Delta y\) is the change in the number of pages in the copy machine, and \(\Delta x\) is the change in time.

Using the first two points (0 seconds, 500 pages) and (2 seconds, 495 pages):

\[
\Delta y = 495 - 500 = -5 \quad \text{(pages)}
\]
\[
\Delta x = 2 - 0 = 2 \quad \text{(seconds)}
\]

Now, substituting these values into the slope formula:

\[
\text{slope} = \frac{-5}{2} = -2.5 \quad \text{(pages per second)}
\]

Next, if we consider the change from 0 to 4 seconds (the last point):

Using points (0 seconds, 500 pages) and (4 seconds, 490 pages):

\[
\Delta y = 490 - 500 = -10 \quad \text{(pages)}
\]
\[
\Delta x = 4 - 0 = 4 \quad \text{(seconds)}
\]

Calculating the slope again:

\[
\text{slope} = \frac{-10}{4} = -2.5 \quad \text{(pages per second)}
\]

Now, the amounts we've observed describe the same situation in different intervals but reflect a uniform change.

To present the information in a more practical context:

1. The rate of change indicates that the copy machine is reducing its pages at a rate of **−5 pages every 2 seconds**. This is the most simplified representation of the rate from the choices provided.

Thus, the correct answer among the provided options is:

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