Which of the following tables represents a proportional relationship?

Question

A.
x 2 3 4 5
y 3 6 9 12

B.
x 2 4 6 8
y 3 4 5 6

C.
x 2 4 6 8
y 3 6 9 12

D.
x 1 4 7 10
y 0 3 6 9

Answer 1

To determine which of the tables represents a proportional relationship, we need to check if the ratio of \( y \) to \( x \) is constant for each pair of values in the table.

Table A:

• \( (2, 3) \): \( \frac{3}{2} = 1.5 \)
• \( (3, 6) \): \( \frac{6}{3} = 2 \)
• \( (4, 9) \): \( \frac{9}{4} = 2.25 \)
• \( (5, 12) \): \( \frac{12}{5} = 2.4 \)

Not proportional (different ratios).

Table B:

• \( (2, 3) \): \( \frac{3}{2} = 1.5 \)
• \( (4, 4) \): \( \frac{4}{4} = 1 \)
• \( (6, 5) \): \( \frac{5}{6} \approx 0.833 \)
• \( (8, 6) \): \( \frac{6}{8} = 0.75 \)

Not proportional (different ratios).

Table C:

• \( (2, 3) \): \( \frac{3}{2} = 1.5 \)
• \( (4, 6) \): \( \frac{6}{4} = 1.5 \)
• \( (6, 9) \): \( \frac{9}{6} = 1.5 \)
• \( (8, 12) \): \( \frac{12}{8} = 1.5 \)

Proportional (constant ratio of 1.5).

Table D:

• \( (1, 0) \): \( \frac{0}{1} = 0 \)
• \( (4, 3) \): \( \frac{3}{4} = 0.75 \)
• \( (7, 6) \): \( \frac{6}{7} \approx 0.857 \)
• \( (10, 9) \): \( \frac{9}{10} = 0.9 \)

Not proportional (different ratios).

Conclusion:

Table C represents a proportional relationship.