Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which of the following statements describes a proportional relationship?

1. The graph passes through the origin

2. Both quantities have different rates

3. The increase is irregular

4. Both quantities decrease simultaneously

The correct answer is: The graph passes through the origin

A proportional relationship is characterized by a constant ratio between two quantities. When graphed, these relationships produce a straight line that passes through the origin. This is because, at the origin, both quantities are zero, indicating that there is no value unless both quantities are present in a relevant ratio. Therefore, the key feature of a proportional relationship is that for any increase in one quantity, there is a corresponding increase in the other at a consistent rate. In contrast, different rates in quantities imply a non-proportional relationship, as variations in one quantity would not consistently reflect the same change in the other. Irregular increases indicate that the change between the two quantities is not predictable or consistent, which again moves away from the definition of proportionality. Finally, while simultaneous decreases can occur in a proportional relationship, it does not encapsulate the essential characteristic that defines proportionality, which is the consistent ratio maintained amid changes.