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Question

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)
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Answer 1

A proportional relationship is one where the ratio of the two quantities remains constant, which can also be visually represented by a straight line passing through the origin on a graph.

Looking at the lines on the graph:

• Line 1: Starts at (0, 2), so it does not pass through the origin. This indicates it's not proportional.
• Line 2: Starts at (0, 0), which suggests it could be proportional, and the points (0,0), (2,3), (4,7), and (5,8) can be analyzed for a constant ratio, but the increase is not consistent.
• Line 3: Also starts at (0, 0) and the points (0,0), (2,2), (4,4), and (7,7) do maintain a consistent ratio of levels passed to time. For instance, for every 2 minutes, they pass 2 levels, maintaining a constant rate.

Since Line 3 is the only line that starts at the origin and shows consistent ratios, it represents a proportional relationship.

Answer: Line 3