The question asks to identify which graph represents a proportional relationship. In mathematics, a proportional relationship is one in which two quantities increase or decrease at the same rate, typically following the equation:

$y = kx$

Where $k$ is the constant of proportionality. A graph representing a proportional relationship is a straight line that passes through the origin (0,0).

Let's analyze each graph:

• Graph A: This is a straight line that passes through the origin. It indicates a proportional relationship since it follows the form $y = kx$.

• Graph B: Although this is a straight line, it does not pass through the origin, so it is not a proportional relationship.

• Graph C: This graph is a curve and does not represent a straight line, so it cannot represent a proportional relationship.

• Graph D: This is also a curve, and like Graph C, it does not represent a proportional relationship.

Conclusion:

Graph A represents a proportional relationship because it is a straight line passing through the origin.

Would you like further clarification, or do you have any other questions?

Here are 5 related questions for further practice:

1. How do you determine the constant of proportionality from a graph?
2. Can a line that doesn’t pass through the origin still represent a linear relationship?
3. How do you distinguish between a proportional and non-proportional linear relationship?
4. What is the equation for a direct proportionality relationship?
5. What is the difference between linearity and proportionality?

Tip: For a graph to represent a proportional relationship, always check if it is a straight line passing through the origin.