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A graph with the x-axis representing time in minutes ranging from 0 to 10 in increments of 1, and the y-axis representing levels passed ranging from 0 to 10 in increments of 1 shows three lines labeled 1, 2 and 3. Line 1 passes through the following points: left parenthesis 0 comma 2 right parenthesis; left parenthesis 2 comma 5 right parenthesis; and left parenthesis 4 comma 8 right parenthesis. Line 2 passes through the following points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; left parenthesis 4 comma 7 right parenthesis; and left parenthesis 5 comma 8 right parenthesis. Line 3 passes through the following points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 2 right parenthesis; left parenthesis 4 comma 4 right parenthesis; and left parenthesis 7 comma 7 right parenthesis.

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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1 answer

To determine which friend's graph represents a proportional relationship, we need to identify if there is a consistent ratio between the time played (x-axis) and the levels passed (y-axis) for each friend.

A proportional relationship means that as the time increases, the levels passed increase at a constant rate, and the line will pass through the origin (0,0).

  • Line 1 starts at (0,2), which means it does not pass through the origin. This indicates it does not represent a proportional relationship.

  • Line 2 starts at (0,0) and appears to have a consistent increase in levels passed relative to time played. This line seems to show a proportional relationship because it passes through the origin and increases at a consistent rate.

  • Line 3 also starts at (0,0) but does not maintain a consistent ratio as clearly as Line 2.

Given this analysis, Line 2 represents a proportional relationship because it starts at the origin and maintains a consistent ratio between time and levels passed. Therefore, the friend corresponding to Line 2 is the one with a proportional relationship.