To determine whether the line that passes through the given coordinates represents a proportional relationship, we first need to understand what a proportional relationship is.
In a proportional relationship, the ratio of the y-values to the x-values is constant, and the line representing this relationship passes through the origin (0, 0).
Let's examine the given coordinates one by one:
- For (2, 3), the ratio is \( \frac{3}{2} = 1.5 \)
- For (3, 4.5), the ratio is \( \frac{4.5}{3} = 1.5 \)
- For (4, 6), the ratio is \( \frac{6}{4} = 1.5 \)
- For (6, 9), the ratio is \( \frac{9}{6} = 1.5 \)
Since the ratio \( \frac{y}{x} \) is constant and equals 1.5 for all points, it indicates a linear relationship.
Now, we also need to check if this line passes through the origin. The original given coordinates (2, 3), (3, 4.5), (4, 6), and (6, 9) do not include the origin (0, 0), and therefore the line represented by connecting these points will not pass through the origin.
Conclusion:
- The line does not pass through the origin.
- Therefore, it does not represent a proportional relationship.
Based on the options provided:
The correct answer is: B. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
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