To determine which table demonstrates a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all pairs of \( (x, y) \).
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Table 1:
- \( \frac{2}{10} = 0.2 \)
- \( \frac{3}{15} = 0.2 \)
- \( \frac{8}{40} = 0.2 \)
- Constant ratio: 0.2
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Table 2:
- \( \frac{2}{8} = 0.25 \)
- \( \frac{3}{12} = 0.25 \)
- \( \frac{4}{40} = 0.1 \)
- Not a constant ratio.
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Table 3:
- \( \frac{2}{4} = 0.5 \)
- \( \frac{3}{9} = \frac{1}{3} \approx 0.333 \)
- \( \frac{4}{16} = 0.25 \)
- Not a constant ratio.
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Table 4:
- \( \frac{10}{2} = 5 \)
- \( \frac{20}{5} = 4 \)
- \( \frac{30}{6} = 5 \)
- Not a constant ratio.
The only table that demonstrates a proportional relationship is Table 1, where the ratio \( \frac{y}{x} \) is constant at 0.2.