A worker is packing items in a boxes. The table shows the linear relationship between the number of items the worker has packed in boxes after different amounts of time.

Question

The worker packed 3 items in boxes per minutes
The worker packed 8 items in boxes per minutes
The worker packed 12 items in boxes per minutes
The worker packed 16 items in boxes per minutes

Answer 1

Based on the given information, we can create a linear relationship between the number of items packed and the time.

- For every 1 minute, the worker packed 3 items in boxes.
- For every 1 minute, the worker packed 8 items in boxes.
- For every 1 minute, the worker packed 12 items in boxes.
- For every 1 minute, the worker packed 16 items in boxes.

This linear relationship can be expressed using the equation y = mx + b, where y is the number of items packed, x is the time in minutes, m is the rate of packing items, and b is the initial number of items packed.

From the given data, we can find the value of m (rate of packing items).

For the first data point, when x = 1 minute, y = 3 items.
Using the equation y = mx + b, we have 3 = 1 * m + b.

For the second data point, when x = 1 minute, y = 8 items.
Using the equation y = mx + b, we have 8 = 1 * m + b.

For the third data point, when x = 1 minute, y = 12 items.
Using the equation y = mx + b, we have 12 = 1 * m + b.

For the fourth data point, when x = 1 minute, y = 16 items.
Using the equation y = mx + b, we have 16 = 1 * m + b.

By solving these equations simultaneously, we can find the values of m and b, which will give us the linear relationship between the number of items packed and time. However, since the values for b are not given, we cannot determine the exact linear relationship.