To determine the rate of change of the number of items packed in boxes with respect to the amount of time in minutes, we need to look for the slope of the linear relationship presented in the table. The slope (or rate of change) can be calculated by finding the change in the number of items packed divided by the change in time.
The general formula for the slope (rate of change, \( m \)) in a linear equation is:
\[ m = \frac{\Delta y}{\Delta x} = \frac{\text{Change in items packed}}{\text{Change in time (minutes)}} \]
If the table provides specific values of items packed and corresponding time, you can select two points from the table, usually in the form of \((x_1, y_1)\) and \((x_2, y_2)\), where \(x\) represents time in minutes and \(y\) represents the number of items packed.
For instance, if the table shows:
- 10 items packed in 2 minutes
- 20 items packed in 4 minutes
Using these points:
- \(x_1 = 2, y_1 = 10\)
- \(x_2 = 4, y_2 = 20\)
We can calculate the slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20 - 10}{4 - 2} = \frac{10}{2} = 5 \]
This means that the worker packs 5 items per minute.
In summary, the statement that describes the rate of change of the number of items packed in boxes with respect to the number of minutes would be: "The worker packs boxes at a rate of X items per minute," where X is the value calculated from the table data.
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