https://file.aiquickdraw.com/mathbot/file/1730323908627dov5kafh.jpg

To solve this question, let's analyze the information provided:

1. **Given Information**:
   - The graph represents the number of jars filled by two machines over time.
   - The equation for **Machine A** is \( y = 3x \), where \( y \) represents the number of jars and \( x \) represents the time in minutes.
   
2. **Question**:
   - We need to determine the equation representing the number of jars filled by **Machine B**.

3. **Approach**:
   - From the graph, we can observe the slopes of the lines for both machines:
     - The line for **Machine A** has a slope of 3, which matches \( y = 3x \).
     - The line for **Machine B** has a steeper slope than Machine A, meaning the rate at which Machine B fills jars is higher than Machine A’s rate.
   - Let's check the slopes of the options provided to find the correct rate for Machine B.
   
4. **Options Analysis**:
   - Option \( y = 1.5x \): This slope (1.5) is less than that of Machine A (3), which does not fit since Machine B has a steeper line.
   - Option \( y = 3x \): This is the equation for Machine A, so it cannot represent Machine B.
   - Option \( y = 6x \): This slope (6) is twice the slope of Machine A (3), which aligns with the steeper line for Machine B.
   - Option \( y = 8x \): This slope (8) is even steeper but may be too high compared to the graph’s representation.

5. **Conclusion**:
   - The best answer is **\( y = 6x \)**, as it accurately represents the steeper slope observed for Machine B on the graph.

Would you like a more detailed breakdown of this solution?

### Related Questions:
1. What does the slope represent in the context of this problem?
2. How can you determine the rate of a machine from a graph?
3. Why is the equation \( y = 3x \) suitable for Machine A?
4. How would you interpret a line with a slope of zero in a similar graph?
5. What happens if Machine B's rate changes to match Machine A?

**Tip**: When analyzing a line in a graph, the slope (rise over run) tells you the rate of change, which is crucial in understanding how quickly something is happening over time.

Which equation could represent the number of jars filled by Machine B based on the given graph and the equation y = 3x for Machine A?

Learn how to find the correct linear equation for Machine B based on a graph comparing the rates of jar filling by two machines. This question focuses on understanding slope and graph interpretation for linear equations, suitable for Grades 7-9 students.

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