A worker is packing items in a boxes. The table shows the linear relationship between the number of items the worker has packed in boxes after different amounts of time.

Number of minutes l Number of items packed
4 l 20
6 l 26
12 l 44
14 l 50
Which statement describes the rate of change of the number of items the worker packed in boxes with respect to the number of minutes the worker has been packing items in boxes?
The worker packed 3 items in boxes per minute.
The worker packed 8 items in boxes per minute.
The worker packed 12 items in boxes per minute.
The worker packed 16 items in boxes per minute.

1 answer

To find the rate of change, we can take the difference in the number of items packed and divide it by the difference in time.

Between 4 minutes and 6 minutes, the worker packed 26 - 20 = 6 items.
Between 6 minutes and 12 minutes, the worker packed 44 - 26 = 18 items.
Between 12 minutes and 14 minutes, the worker packed 50 - 44 = 6 items.

Therefore, the rate of change is 6 items / 2 minutes = 3 items per minute.

The statement that describes the rate of change is: The worker packed 3 items in boxes per minute.