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.
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?
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