https://file.aiquickdraw.com/mathbot/file/1730148321688e7niuhlb.jpg

To solve this problem, we need to find how many boxes the machine packages in 6 minutes using the proportional relationship shown in the graph.

1. From the graph, we can see that the line passes through the point (4, 140), meaning that in 4 minutes, the machine packages 140 boxes.
2. Using this point, we can determine the rate of packaging:  
   \[
   \text{Rate} = \frac{\text{Number of boxes}}{\text{Time}} = \frac{140 \text{ boxes}}{4 \text{ minutes}} = 35 \text{ boxes per minute}
   \]
3. To find the number of boxes packaged in 6 minutes, we multiply the rate by 6:
   \[
   \text{Boxes in 6 minutes} = 35 \text{ boxes/minute} \times 6 \text{ minutes} = 210 \text{ boxes}
   \]

So, the machine packages **210 boxes in 6 minutes**.

Would you like more details on the steps, or do you have any other questions?

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Here are some related questions to explore:

1. How many boxes would the machine package in 10 minutes?
2. If the machine packaged 280 boxes, how much time would it have taken?
3. What is the unit rate, or rate of packaging per minute?
4. How would the graph look if the machine’s packaging speed increased?
5. If the machine packaged at 50 boxes per minute, how many boxes would it complete in 5 minutes?

**Tip:** In proportional relationships, the rate or slope remains constant, allowing easy predictions at different points.

The graph shows a proportional relationship between time and number of boxes a machine packages. How many boxes does the machine package in 6 minutes?

Solve a proportional relationship problem by analyzing a graph showing the time and number of boxes a machine packages. Learn how to determine the rate of packaging and calculate the total boxes packaged in 6 minutes. Ideal for Grade 7 math students.

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