To determine which statement best describes the graphs, we need to analyze each graph's characteristics regarding proportional relationships.
A proportional relationship is one where the ratio between the two variables remains constant, and the line representing the relationship passes through the origin (0, 0).
Graph 1 passes through the points (0, 3) and (2, 6):
- The point (0, 3) indicates that when the independent variable is 0, the dependent variable is 3. This means the line does not pass through the origin, indicating it is not a proportional relationship.
Graph 2 passes through the points (0, 0), (1, 5), and (2, 10):
- The point (0, 0) shows that the line passes through the origin. Next, we can check the ratios:
- From (0, 0) to (1, 5): the ratio is \( \frac{5-0}{1-0} = 5 \).
- From (0, 0) to (2, 10): the ratio is \( \frac{10-0}{2-0} = 5 \).
- Both ratios remain constant and equal to 5, confirming that this graph does represent a proportional relationship.
Based on this analysis, the conclusion is: Graph 1 does not represent a proportional relationship, while Graph 2 does.
Therefore, the best statement to describe the graphs is: Graph 2 represents a proportional relationship, but graph 1 does not.
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