https://file.aiquickdraw.com/mathbot/file/17248833378471473y4fi.jpg

Is this graph proportional or non- proportional?

To determine if the graph represents a proportional relationship, we need to check two main characteristics:

1. **The Line Passes Through the Origin (0,0)**: A proportional relationship must pass through the origin, meaning when \( x = 0 \), \( y \) must also equal 0.
   
2. **The Line is Straight**: A proportional relationship will always produce a straight line, indicating a constant rate of change between the variables.

From the image you provided:

- The line appears to be straight, which satisfies one of the conditions for proportionality.
- However, I need to confirm if the line passes through the origin. Based on the image, it seems like the line does pass through the origin, but it's not completely clear. If it does indeed pass through the origin, then the relationship is proportional.

If the line **does** pass through the origin and is straight, the relationship is proportional. If it **does not** pass through the origin, then it is non-proportional.

Would you like to clarify or have any questions about this?

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Here are five related questions:
1. What is the significance of the origin in determining proportionality?
2. How does the slope of the line relate to the constant of proportionality?
3. What happens to the proportionality if the line is curved instead of straight?
4. Can a non-proportional relationship still have a linear equation?
5. How can you use the graph to find the constant of proportionality?

**Tip**: When analyzing a graph for proportionality, always check if the line is straight and if it passes through the origin.

Explore how to determine if a graph represents a proportional relationship. Understand key concepts like the origin, linearity, and constant rate of change. Analyze a specific graph to determine if it is proportional or non-proportional.

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