To describe the rate of change of the number of items the worker has packed in boxes with respect to the number of minutes, you need to establish the relationship from the data in the table. Generally, the rate of change in a linear relationship can be determined by finding the slope of the line formed by the data points.
The slope (rate of change) can be calculated using the formula:
\[ \text{Slope (Rate of Change)} = \frac{\Delta y}{\Delta x} \]
where:
- \( \Delta y \) is the change in the number of items packed,
- \( \Delta x \) is the change in time in minutes.
If the table provided specific values for the number of items and the time, you would:
- Identify two points from the table. For example, if at 1 minute, the worker packed 5 items and at 3 minutes, the worker packed 15 items, the two points would be (1, 5) and (3, 15).
- Calculate the change in items packed (\( \Delta y \)): \[ \Delta y = 15 - 5 = 10 \]
- Calculate the change in time (\( \Delta x \)): \[ \Delta x = 3 - 1 = 2 \]
- Substitute into the slope formula: \[ \text{Slope} = \frac{10}{2} = 5 \]
This result indicates that the worker packs, on average, 5 items per minute.
Thus, without the specific values from your table, you should look for a similar method to determine the rate of change from your linear data, which will describe how many items the worker packs per minute as time progresses. Once you've calculated that, the statement you provide could be that "the worker packs an average of X items per minute," where X is your calculated rate of change.
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