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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?

(1 point)

1 answer

A proportional relationship is characterized by a straight line that passes through the origin (0,0) and has a constant ratio between the two quantities being measured.

Looking at the graphs:

  • Line 1 starts at (0,2) and does not pass through the origin, so it is not proportional.
  • Line 2 passes through (0,0) and appears to increase linearly as time progresses, suggesting a constant rate. Hence, this line represents a proportional relationship.
  • Line 3 also passes through (0,0) but does not maintain a constant rate throughout the time intervals.

Therefore, the friend whose graph is a proportional relationship is Friend 2.