To determine which table uses the same ratio as the given table, we first need to find the ratio of \(y\) to \(x\) from the original table. The pairs of values can be analyzed as follows:
-
For \( (2, 6) \):
\(\frac{y}{x} = \frac{6}{2} = 3\) -
For \( (5, 15) \):
\(\frac{y}{x} = \frac{15}{5} = 3\) -
For \( (8, 24) \):
\(\frac{y}{x} = \frac{24}{8} = 3\) -
For \( (11, 33) \):
\(\frac{y}{x} = \frac{33}{11} = 3\)
All pairs give the same ratio of \(3\).
Now, we will check each of the options A, B, C, and D to see if they maintain the ratio of \(3\).
Option A:
- \( (3, 7) \): \(\frac{7}{3} \approx 2.33\)
- \( (5, 16) \): \(\frac{16}{5} = 3.2\)
- \( (9, 25) \): \(\frac{25}{9} \approx 2.78\)
- \( (12, 34) \): \(\frac{34}{12} \approx 2.83\)
None match the ratio of 3.
Option B:
- \( (4, 8) \): \(\frac{8}{4} = 2\)
- \( (5, 10) \): \(\frac{10}{5} = 2\)
- \( (8, 16) \): \(\frac{16}{8} = 2\)
- \( (13, 26) \): \(\frac{26}{13} = 2\)
None match the ratio of 3.
Option C:
- \( (4, 6) \): \(\frac{6}{4} = 1.5\)
- \( (10, 15) \): \(\frac{15}{10} = 1.5\)
- \( (16, 24) \): \(\frac{24}{16} = 1.5\)
- \( (22, 33) \): \(\frac{33}{22} = 1.5\)
None match the ratio of 3.
Option D:
- \( (3, 9) \): \(\frac{9}{3} = 3\)
- \( (4, 12) \): \(\frac{12}{4} = 3\)
- \( (9, 27) \): \(\frac{27}{9} = 3\)
- \( (12, 36) \): \(\frac{36}{12} = 3\)
All pairs in this option match the ratio of 3.
Thus, the table that uses the same ratio as the original table is Option D.