To determine which representation does not show a proportional relationship between \(x\) and \(y\), we need to check if the ratio \(\frac{y}{x}\) is constant for each set of data.
For option A:
- \((11, 22)\): \(\frac{22}{11} = 2\)
- \((14, 28)\): \(\frac{28}{14} = 2\)
- \((19, 38)\): \(\frac{38}{19} = 2\)
- \((26, 52)\): \(\frac{52}{26} = 2\)
All ratios are equal to 2, so option A shows a proportional relationship.
For option D:
- \((14, 77)\): \(\frac{77}{14} = 5.5\)
- \((16, 88)\): \(\frac{88}{16} = 5.5\)
- \((18, 1515)\): \(\frac{1515}{18} \approx 84.1667\)
- \((20, 1414)\): \(\frac{1414}{20} = 70.7\)
The ratios are not constant (the third and fourth entries are especially different from the first two), indicating that option D does not show a proportional relationship.
Final Answer: D
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