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.