To determine which table represents a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) remains constant for all corresponding \( x \) and \( y \) values in each table.
Let's examine each table:
A:
- For \( (2, 3) \): \( \frac{3}{2} = 1.5 \)
- For \( (3, 6) \): \( \frac{6}{3} = 2 \)
- For \( (4, 9) \): \( \frac{9}{4} = 2.25 \)
- For \( (5, 12) \): \( \frac{12}{5} = 2.4 \)
The ratios are not constant, so table A does not represent a proportional relationship.
B:
- For \( (2, 3) \): \( \frac{3}{2} = 1.5 \)
- For \( (4, 6) \): \( \frac{6}{4} = 1.5 \)
- For \( (6, 9) \): \( \frac{9}{6} = 1.5 \)
- For \( (8, 12) \): \( \frac{12}{8} = 1.5 \)
All the ratios are equal to \( 1.5 \), so table B does represent a proportional relationship.
C:
- For \( (1, 0) \): \( \frac{0}{1} = 0 \)
- For \( (4, 3) \): \( \frac{3}{4} = 0.75 \)
- For \( (7, 6) \): \( \frac{6}{7} \approx 0.857 \)
- For \( (10, 9) \): \( \frac{9}{10} = 0.9 \)
The ratios are not constant, so table C does not represent a proportional relationship.
D:
- For \( (2, 3) \): \( \frac{3}{2} = 1.5 \)
- For \( (4, 4) \): \( \frac{4}{4} = 1 \)
- For \( (6, 5) \): \( \frac{5}{6} \approx 0.833 \)
- For \( (8, 6) \): \( \frac{6}{8} = 0.75 \)
The ratios are not constant, so table D does not represent a proportional relationship.
In conclusion, the only table that represents a proportional relationship is B.
4 answers