https://file.aiquickdraw.com/mathbot/file/1727817348528wsgp7qh8.jpg

Let's analyze each graph to determine if \(x\) and \(y\) are proportional.

### Graph 1:
In Graph 1, we observe that the line passes through the origin (0,0) and forms a straight line. This suggests a proportional relationship between \(x\) and \(y\).

- The slope of the line gives us the constant of proportionality. From the graph, when \(x = 2\), \(y = 6\). The ratio \( \frac{y}{x} = \frac{6}{2} = 3 \), so \(y\) is 3 times \(x\).

Thus, **Graph 1 is proportional**, and the relationship is \( y = 3x \).

### Graph 2:
In Graph 2, the line does not pass through the origin, which is a key requirement for proportionality. Even though the line is straight, the fact that it doesn't pass through the origin means that \(x\) and \(y\) are not proportional.

Thus, **Graph 2 is not proportional**.

### Graph 3:
In Graph 3, the graph shows a vertical line. This means that the value of \(x\) remains the same (specifically \(x = 2\)) while \(y\) changes. This clearly indicates there is no proportional relationship between \(x\) and \(y\).

Thus, **Graph 3 is not proportional**.

### Conclusion:
1. **Graph 1**: Proportional, \(y = 3x\)
2. **Graph 2**: Not proportional
3. **Graph 3**: Not proportional

Would you like more details or have any questions?

Here are 5 follow-up questions to expand on this information:
1. How can we find the constant of proportionality from a graph?
2. Why must a proportional relationship pass through the origin?
3. How does the slope of the line relate to proportionality?
4. Can a non-linear graph ever represent a proportional relationship?
5. How can we check proportionality algebraically from given points?

**Tip:** A proportional relationship is always represented by a straight line passing through the origin. Keep an eye on both these conditions!

Each graph below shows a relationship between x and y. For each graph, determine whether x and y are proportional. If x and y are proportional, fill in the blank with a number in simplest form.

Learn how to identify proportional relationships by analyzing three graphs representing the relationship between x and y. This problem covers the key concepts of proportionality, including how to determine if x and y maintain a constant ratio and whether the line passes through the origin. Suitable for students in Grades 6-8.

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