Question

Cathy attended a birthday party where the guests took their shoes off to jump in a bouncy castle. She made this graph to compare the number of people at the party to the shoes on the rack. What statement best describes the relationship? A. The relationship is not proportional because the graph does not continue forever. B. The relationship is not proportional because it does not include negative values. C. The relationship is proportional because its graph is a straight line through the origin. D. The relationship is proportional because the number of shoes is always greater than the number of people.

Answer 1

The best statement describing the relationship based on the information provided is:

C. The relationship is proportional because its graph is a straight line through the origin.

A proportional relationship means that one quantity is directly proportional to another, which results in a straight line passing through the origin on a graph. In this case, the number of people at the party is directly related to the number of shoes on the rack since guests took off their shoes before jumping on the bouncy castle.

Answer 2

The best statement describing the relationship is C. The relationship is proportional because its graph is a straight line through the origin.

A proportional relationship is a type of relationship in which two quantities are directly proportional to each other. This means that as one quantity increases, the other quantity increases by the same factor. For example, if you double the amount of money you spend on groceries, you will also double the amount of groceries you get.

In the graph you provided, the number of people and the number of shoes are directly proportional to each other. This means that as the number of people increases, the number of shoes also increases by the same factor. The graph of this relationship is a straight line through the origin, which is a classic sign of a proportional relationship.