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.