Worksheet identifying proportional and non-proportional relationships through graph analysis.

To solve this problem, we need to determine whether each graph represents a proportional or non-proportional relationship based on the key rule:

> A proportional relationship passes through the origin (0, 0).
> A non-proportional relationship does not pass through the origin.

We will examine each graph and check if it goes through the point (0, 0).

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✔ Step-by-step analysis:

#### Graph 1
- The line crosses the y-axis at a point above the origin (around y = 2).
- It does not pass through (0, 0).
- Answer: non-proportional

#### Graph 2
- The line passes through the origin (0, 0).
- It is a straight line going through the center.
- Answer: proportional

#### Graph 3
- The line appears to cross the y-axis at a positive value (around y = 4).
- It does not go through (0, 0).
- Answer: non-proportional

#### Graph 4
- The line crosses the y-axis below the origin (around y = -2).
- It does not pass through (0, 0).
- Answer: non-proportional

#### Graph 5
- The line passes through the origin (0, 0).
- It's a straight line starting from the origin and extending in both directions.
- Answer: proportional

#### Graph 6
- The line crosses the y-axis at a negative value (around y = -1).
- It does not pass through (0, 0).
- Answer: non-proportional

#### Graph 7
- The line passes through the origin (0, 0).
- It’s a straight diagonal line going through the center.
- Answer: proportional

#### Graph 8
- The line passes through the origin (0, 0).
- Even though it's steep, it clearly goes through (0, 0).
- Answer: proportional

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✔ Final Answers (Circle the correct word):

1. non-proportional
2. proportional
3. non-proportional
4. non-proportional
5. proportional
6. non-proportional
7. proportional
8. proportional

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📌 Summary:

| Graph | Relationship |
|-------|--------------------|
| 1 | non-proportional |
| 2 | proportional |
| 3 | non-proportional |
| 4 | non-proportional |
| 5 | proportional |
| 6 | non-proportional |
| 7 | proportional |
| 8 | proportional |

✔ All decisions are based on whether the graph passes through the origin (0, 0).