Question

Which of the following tables represents a proportional relationship?
A.
x 8 12 16 24
y 10 15 25 30


B.
x 12 18 30 36
y 12 24 36 48


C.
x 12 18 30 36
y 4 8 16 24


D.
x 12 18 30 36
y 10 15 25 30

Answer 1

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.