Which linear graph represents a proportional relationship?

A graph of a straight line that passes through the points 0 comma 2 and 1 comma 2.
A graph of a straight line that passes through the points negative 1 comma 0 and negative 1 comma 1.
A graph of a straight line that passes through the points 0 comma 0 and 1 comma negative 2.
A graph of a straight line that passes through the points 0 comma 2 and 2 comma 3.

To determine which linear graph represents a proportional relationship, we need to consider the key characteristic of proportional relationships: **the graph must be a straight line that passes through the origin (0, 0)**.

Let's analyze each option:

1. **Graph that passes through the points (0, 2) and (1, 2)**:
   - This line is horizontal, meaning it has a constant y-value of 2. 
   - It does **not** pass through the origin (0, 0).
   - **Not a proportional relationship.**

2. **Graph that passes through the points (-1, 0) and (-1, 1)**:
   - This line is vertical, meaning it has a constant x-value of -1.
   - It does **not** pass through the origin (0, 0).
   - **Not a proportional relationship.**

3. **Graph that passes through the points (0, 0) and (1, -2)**:
   - This line passes through the origin (0, 0).
   - The y-values change proportionally with the x-values.
   - **This is a proportional relationship.**

4. **Graph that passes through the points (0, 2) and (2, 3)**:
   - This line does **not** pass through the origin (0, 0).
   - **Not a proportional relationship.**

### Conclusion:
The graph that represents a proportional relationship is the one that passes through the points **(0, 0) and (1, -2)**.

Would you like further details or have any questions?

### Relative Questions:
1. What is the general form of a proportional relationship equation?
2. How can you determine the slope of a line from two points?
3. Can a line that doesn't pass through the origin still be linear but not proportional?
4. What distinguishes a proportional relationship from other linear relationships?
5. How can the slope of a proportional relationship be interpreted?
6. What are some real-world examples of proportional relationships?
7. How would the equation of the line passing through (0, 0) and (1, -2) look like?
8. What is the significance of the slope in a proportional relationship?

**Tip:** When identifying a proportional relationship in a graph, always check if the line passes through the origin.

Learn how to identify proportional relationships in linear graphs through examples and explanations. Understand the key characteristic of proportional relationships and analyze graphs that pass through specific points. Suitable for students in Grades 6-8.

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