To determine which table uses the same ratio as the original table, we'll first identify the ratio from the original table.
The pairs of values are as follows:
- For (2, 6): the ratio \( \frac{y}{x} = \frac{6}{2} = 3 \)
- For (5, 15): the ratio \( \frac{y}{x} = \frac{15}{5} = 3 \)
- For (8, 24): the ratio \( \frac{y}{x} = \frac{24}{8} = 3 \)
- For (11, 33): the ratio \( \frac{y}{x} = \frac{33}{11} = 3 \)
Thus, the ratio \( \frac{y}{x} = 3 \) is consistent across all pairs in the original table.
Now, we can check the ratios in each of the provided options:
Option A:
- For (3, 7): \( \frac{7}{3} \approx 2.33 \)
- For (5, 16): \( \frac{16}{5} = 3.2 \)
- For (9, 25): \( \frac{25}{9} \approx 2.78 \)
- For (12, 34): \( \frac{34}{12} \approx 2.83 \)
Option B:
- For (4, 8): \( \frac{8}{4} = 2 \)
- For (5, 10): \( \frac{10}{5} = 2 \)
- For (8, 16): \( \frac{16}{8} = 2 \)
- For (13, 26): \( \frac{26}{13} = 2 \)
Option C:
- For (4, 6): \( \frac{6}{4} = 1.5 \)
- For (10, 15): \( \frac{15}{10} = 1.5 \)
- For (16, 24): \( \frac{24}{16} = 1.5 \)
- For (22, 33): \( \frac{33}{22} = 1.5 \)
Option D:
- For (3, 9): \( \frac{9}{3} = 3 \)
- For (4, 12): \( \frac{12}{4} = 3 \)
- For (9, 27): \( \frac{27}{9} = 3 \)
- For (12, 36): \( \frac{36}{12} = 3 \)
From the calculations above, Option D uses the same ratio of \( \frac{y}{x} = 3 \) as in the original table.
Therefore, the answer is D.
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