Question

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.
items packed in boxes

number of minutes	number of items packed
7	28
11	44
14	56

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 37 items in boxes per minute
the worker packed 4 items in boxes per minute
the worker packed 8 items in boxes per minute
the worker packed 15 items in boxes per minute

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x$ be the number of minutes and $y$ be the number of items packed.

Step2: Select two points

Let's take the first two points $(x_1 = 5,y_1=20)$ and $(x_2 = 7,y_2 = 28)$.

Step3: Calculate the rate of change

$m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{28 - 20}{7 - 5}=\frac{8}{2}=4$.
We can check with other points. For example, taking $(x_1 = 11,y_1 = 44)$ and $(x_2=14,y_2 = 56)$, $m=\frac{56 - 44}{14 - 11}=\frac{12}{3}=4$.

Answer:

The worker packed 4 items in boxes per minute