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.
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
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.