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The graph shows a proportional relationship between time (in minutes) and the number of boxes a machine packages. To solve how many boxes the machine can package in 3 minutes, we need to determine the rate of packaging based on the graph.

From the graph:
- At \(x = 8\) minutes, the number of boxes \(y = 160\).

This gives us a rate of:
\[
\text{Rate} = \frac{160 \text{ boxes}}{8 \text{ minutes}} = 20 \text{ boxes per minute}.
\]

Now, for 3 minutes:
\[
\text{Boxes in 3 minutes} = 20 \times 3 = 60 \text{ boxes}.
\]

Thus, the machine packages **60 boxes** in 3 minutes.

Would you like a more detailed breakdown or have any other questions?

Here are five related questions for further exploration:
1. How many boxes does the machine package in 10 minutes?
2. How long does it take the machine to package 100 boxes?
3. If the rate increased to 25 boxes per minute, how many boxes would be packaged in 5 minutes?
4. What would be the equation of the line representing this proportional relationship?
5. How would the graph change if the machine's rate slowed to 15 boxes per minute?

**Tip:** To find the rate of change in graphs like this, divide the change in the number of boxes by the change in time.

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?

Discover how to calculate the number of boxes a machine packages in 3 minutes using proportional relationships. Learn about key math concepts like rates and direct proportionality, perfect for Grades 6-8 students.

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