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.

Question

number of minutes number of items packed

4 20
6 26
12 44
14 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

Answer 1

To determine the rate of change of the number of items packed with respect to the number of minutes, we can calculate the slope of the linear relationship. The rate of change (slope) can be found by selecting two points from the table and using the formula:

\[ \text{slope} = \frac{\text{change in items}}{\text{change in time}} = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's use the points (4, 20) and (14, 50):

• \(x_1 = 4\), \(y_1 = 20\)
• \(x_2 = 14\), \(y_2 = 50\)

Now, plug these values into the slope formula:

\[ \text{slope} = \frac{50 - 20}{14 - 4} = \frac{30}{10} = 3 \]

This means that the rate of change of the number of items packed in boxes with respect to the number of minutes is 3 items per minute.

Thus, the statement that describes the rate of change is: "The worker packs items at a rate of 3 items per minute."