Three friends are playing video games. The graph shows the number of levels passed based on amount of time played. Which friend’s graph (1, 2, or 3) is a proportional relationship?

Answer 1

In order to determine which friend's graph represents a proportional relationship, we need to identify the graph that exhibits a constant rate of change. A proportional relationship is characterized by a constant ratio between the two quantities being compared.

Looking at the graph, let's analyze the rate of change for each friend's data:

- Friend 1: From 0 to 2 hours, 0 levels are passed. From 2 to 4 hours, 2 levels are passed. From 4 to 6 hours, 4 levels are passed. The rate of change is not constant since it increases by 2 levels at each interval.

- Friend 2: From 0 to 2 hours, 0 levels are passed. From 2 to 4 hours, 4 levels are passed. From 4 to 6 hours, 6 levels are passed. The rate of change is not constant since it increases by different amounts at each interval.

- Friend 3: From 0 to 2 hours, 0 levels are passed. From 2 to 4 hours, 2 levels are passed. From 4 to 6 hours, 4 levels are passed. The rate of change is constant, increasing by 2 levels at each interval.

Based on this analysis, we can conclude that Friend 3's graph represents a proportional relationship, as the rate of change is constant.