To determine the slope from the data given:
The x-values represent time in seconds, and the y-values represent the number of pages in the copy machine. The points in the table are:
- (0, 500)
- (2, 495)
- (4, 490)
To find the slope (m) between the points (0, 500) and (2, 495), we use the formula for slope, which is:
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the values:
\[ m = \frac{495 - 500}{2 - 0} = \frac{-5}{2} = -2.5 \]
Now, if we look at the slope as a rate:
A slope of \(-2.5\) pages per second can be interpreted in context: the copy machine is losing pages (i.e., the number of pages is decreasing) as time passes.
To convert this into a more simplified rate using whole numbers, we can say that the machine loses 5 pages every 2 seconds.
Thus, the most appropriate interpretation of the slope from the options provided is:
The slope is −5 pages in the copy machine every 2 seconds.