To determine which table of ordered pairs represents a proportional relationship, we need to check if the ratio of \( y \) to \( x \) (i.e., \(\frac{y}{x}\)) is constant for all entries in the table.
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First table (x: -2, -4, -6; y: 4, 16, 36):
- \(\frac{4}{-2} = -2\)
- \(\frac{16}{-4} = -4\)
- \(\frac{36}{-6} = -6\)
- Ratios are not constant.
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Second table (x: -4, -6, -8; y: -8, -12, -18):
- \(\frac{-8}{-4} = 2\)
- \(\frac{-12}{-6} = 2\)
- \(\frac{-18}{-8} = 2.25\)
- Ratios are not constant.
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Third table (x: -3, -5, -7; y: 5, 3, 1):
- \(\frac{5}{-3} \approx -1.67\)
- \(\frac{3}{-5} = -0.6\)
- \(\frac{1}{-7} \approx -0.14\)
- Ratios are not constant.
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Fourth table (x: -3, -6, -9; y: 12, 24, 36):
- \(\frac{12}{-3} = -4\)
- \(\frac{24}{-6} = -4\)
- \(\frac{36}{-9} = -4\)
- Ratios are constant.
Thus, the table that represents a proportional relationship is the fourth table:
- x: -3, -6, -9
- y: 12, 24, 36