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

the slope is -5 pages in the copy machine every 2 seconds
the slope is 2 pages in the copy machine every 5 seconds
the slope is 500 pages in the copy machine
the slope is -5 pages every second

Answer 1

To interpret the slope in the context of the situation given the values in the table, we first need to determine the slope using the two points provided (0, 500) and (2, 495).

The slope (\( m \)) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \( (x_1, y_1) = (0, 500) \) and \( (x_2, y_2) = (2, 495) \).

Substituting in the values:

\[
m = \frac{495 - 500}{2 - 0} = \frac{-5}{2}
\]

This slope of \(-\frac{5}{2}\) represents the rate at which pages are being used or depleted in the copy machine per second.

To simplify this, we convert \(-\frac{5}{2}\) to a whole number rate. The negative sign indicates that pages are decreasing.

To express this in a more straightforward way:
- The slope \(-\frac{5}{2}\) means that every 2 seconds, 5 pages are used.
- Thus, the rate can be converted to a per second rate:
\(-\frac{5}{2} = -2.5\) pages per second.

Since we are looking for the most simplified rate using whole numbers, we can state:

**The slope is -5 pages every 2 seconds.**

This matches your first option.