A proportional relationship is one where the ratio of \(y\) to \(x\) is constant. To determine if any of the given tables represent a proportional relationship, we can calculate the ratios \( \frac{y}{x} \) for each pair of values.
Let's check each option:
Option A:
- For (8, 10): \( \frac{10}{8} = 1.25 \)
- For (12, 15): \( \frac{15}{12} = 1.25 \)
- For (16, 25): \( \frac{25}{16} = 1.5625 \)
- For (24, 30): \( \frac{30}{24} = 1.25 \)
Not all ratios are equal, so this is not proportional.
Option B:
- For (12, 12): \( \frac{12}{12} = 1 \)
- For (18, 24): \( \frac{24}{18} = \frac{4}{3} \)
- For (30, 36): \( \frac{36}{30} = 1.2 \)
- For (36, 48): \( \frac{48}{36} = \frac{4}{3} \)
Not all ratios are equal, so this is not proportional.
Option C:
- For (12, 4): \( \frac{4}{12} = \frac{1}{3} \)
- For (18, 8): \( \frac{8}{18} = \frac{4}{9} \)
- For (30, 16): \( \frac{16}{30} = \frac{8}{15} \)
- For (36, 24): \( \frac{24}{36} = \frac{2}{3} \)
Not all ratios are equal, so this is not proportional.
Option D:
- For (12, 10): \( \frac{10}{12} = \frac{5}{6} \)
- For (18, 15): \( \frac{15}{18} = \frac{5}{6} \)
- For (30, 25): \( \frac{25}{30} = \frac{5}{6} \)
- For (36, 30): \( \frac{30}{36} = \frac{5}{6} \)
All ratios are equal, so this is a proportional relationship.
Conclusion:
Option D represents a proportional relationship.