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

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.

1 answer

To find the slope, we can use the formula for the slope between two points, which is given by:

\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points \((0, 500)\) and \((2, 495)\):

\[ \Delta y = 495 - 500 = -5 \] \[ \Delta x = 2 - 0 = 2 \]

So, the slope is:

\[ \text{slope} = \frac{-5}{2} \]

This means that for every 2 seconds that pass, the number of pages in the copy machine decreases by 5 pages.

To interpret the slope in the context of the situation, we note that:

  • The slope is \(-5\) pages in the copy machine every 2 seconds.

However, to find the rate per second, we can divide by 2:

\[ \frac{-5 \text{ pages}}{2 \text{ seconds}} = -2.5 \text{ pages per second} \]

Since the interpretations provided are in whole numbers and can be directly derived from the slope over the interval, the response that corresponds with the slope is:

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

This captures the rate at which the pages are decreasing in the machine based on the data provided.