**Which of the following graphs show a proportional relationship?**

Choose all answers that apply:

Choose all answers that apply:

(Choice A)

\[\small{2}\]\[\small{4}\]\[\small{6}\]\[\small{8}\]\[\small{2}\]\[\small{4}\]\[\small{6}\]\[\small{8}\]\[y\]\[x\]

A

\[\small{2}\]\[\small{4}\]\[\small{6}\]\[\small{8}\]\[\small{2}\]\[\small{4}\]\[\small{6}\]\[\small{8}\]\[y\]\[x\]

(Choice B)

\[\small{2}\]\[\small{4}\]\[\small{6}\]\[\small{8}\]\[\small{2}\]\[\small{4}\]\[\small{6}\]\[\small{8}\]\[y\]\[x\]

B

\[\small{2}\]\[\small{4}\]\[\small{6}\]\[\small{8}\]\[\small{2}\]\[\small{4}\]\[\small{6}\]\[\small{8}\]\[y\]\[x\]

(Choice C)

None of the above

C

None of the above

2 of 13

To determine which of the given graphs show a proportional relationship, we need to understand the key characteristics of such a relationship:

1. **Straight Line Passing Through the Origin:** A proportional relationship is represented by a straight line that passes through the origin \((0,0)\).
2. **Constant Ratio:** The ratio \(\frac{y}{x}\) should be constant for all points on the line.

### Let's analyze each option:

- **Choice A:** 
  - If this graph shows a straight line passing through the origin, it would indicate a proportional relationship.
  
- **Choice B:** 
  - The same applies here; a straight line through the origin would suggest proportionality.
  
- **Choice C:**
  - "None of the above" indicates that neither Choice A nor B exhibits proportionality.

### Conclusion:

Without visual details of the graphs, it's difficult to definitively state which option shows a proportional relationship. Generally, if a graph shows a straight line through the origin, then it would be proportional.

If you'd like, you can describe the graphs in more detail or upload an image of them, and I can analyze them more accurately.

Would you like more details or have any questions? 

Here are 5 related questions you might consider:
1. How can you determine the slope of a proportional relationship?
2. What does the constant of proportionality represent?
3. How does a non-proportional linear relationship differ from a proportional one?
4. Can a graph that does not pass through the origin ever be proportional?
5. How can you test whether a set of data points shows a proportional relationship?

**Tip:** In a proportional relationship, every point on the line has coordinates \((x, y)\) such that \(y = kx\), where \(k\) is the constant of proportionality.

Discover how to identify proportional relationships in graphs with clear explanations and examples. Learn about the characteristics of proportional graphs, including straight lines passing through the origin and constant ratios. Suitable for students in Grades 6-8.

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