Question

Interpreting Linear Relationships Quick Check
4 of 54 of 5 Items
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 −5
pages in the copy machine every 2 seconds.
The slope is negative 5 pages in the copy machine every 2 seconds.

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 500 pages in the copy machine.

Answer 1

To interpret the slope based on the table provided, we can calculate it using the change in \(y\) (pages in the copy machine) over the change in \(x\) (time in seconds).

From the table:
- When \(x = 0\), \(y = 500\)
- When \(x = 2\), \(y = 495\)
- When \(x = 4\), \(y = 490\)

Calculating the slope between \(x = 0\) and \(x = 2\):
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{495 - 500}{2 - 0} = \frac{-5}{2} = -2.5
\]
This indicates that the pages are decreasing at a rate of 2.5 pages every second over those 2 seconds.

Calculating the slope between \(x = 2\) and \(x = 4\):
\[
\text{slope} = \frac{490 - 495}{4 - 2} = \frac{-5}{2} = -2.5
\]

So, the overall slope for the situation indicates that the number of pages in the copy machine decreases by 5 pages every 2 seconds.

Thus, the correct interpretation is:

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