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.

1 answer

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.