A worker is packing items in boxes. The table shows the linear relationship between the number of items the worker has packed in boxes after different amounts of time. 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 the boxes
table-
5 20
7 28
11 44
14 56
answer choices
The worker packed 8 items in boxes per minute
The worker packed 37 items in boxes per minute
the worker packed 4 items in boxes per minute
the worker packed15 items in boxes per minute
To determine 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, we need to find the slope of the linear relationship between the number of items packed and the time in minutes.
First, let's calculate the change in the number of items packed:
- From 5 minutes to 7 minutes, 28-20 = 8 items packed
- From 7 minutes to 11 minutes, 44-28 = 16 items packed
- From 11 minutes to 14 minutes, 56-44 = 12 items packed
Now, let's find the average rate of change:
- (8+16+12)/3 = 36/3 = 12 items per minute
Therefore, the worker packed items at a rate of 12 items per minute. None of the provided answer choices align with this rate.