The graph shows a proportional relationship between time and number of boxes a machine packages. How many boxes does the machine package in 3 ​minutes?

Number of Boxes Packaged
0
2
4
6
8
0
80
160
240
320
Time (minutes), x
Number of Boxes, y

x y graph
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Question content area right
Part 1
The machine packages
   boxes in 3 minutes.

1 answer

To determine how many boxes the machine packages in 3 minutes based on the information given in the graph, we need to identify the proportional relationship between time (x-axis) and the number of boxes packaged (y-axis).

From your description, it seems that the graph plots the number of boxes on the y-axis against the time in minutes on the x-axis.

Assuming the relationship is linear (which we can infer from the mention of a proportional relationship) and that we can extract scale values from the y-axis:

From the numbers given:

  • If at \(0\) minutes, \(0\) boxes;
  • At \(1\) minute, \(2\) boxes;
  • At a further minute, \(4\) boxes and so on.

From the pattern, we can see that the machine packages \(2\) boxes per minute.

So, in \(3\) minutes, the machine will package: \[ 2 \text{ boxes/minute} \times 3 \text{ minutes} = 6 \text{ boxes}. \]

Thus, the machine packages 6 boxes in 3 minutes.