To determine whether the relationship between the two sets of values (X and Y) is proportional, we need to check if the ratio of Y to X remains constant across the values given.
The table provided has the following pairs:
- For \( X = -9 \), \( Y = 13.5 \)
- For \( X = -8 \), \( Y = 12 \)
- For \( X = -7 \), \( Y = 10.5 \)
- For \( X = -6 \), \( Y = 9 \)
We can calculate the ratios \( \frac{Y}{X} \) for each pair:
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For \( X = -9 \), \( Y = 13.5 \): \[ \frac{Y}{X} = \frac{13.5}{-9} = -1.5 \]
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For \( X = -8 \), \( Y = 12 \): \[ \frac{Y}{X} = \frac{12}{-8} = -1.5 \]
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For \( X = -7 \), \( Y = 10.5 \): \[ \frac{Y}{X} = \frac{10.5}{-7} = -1.5 \]
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For \( X = -6 \), \( Y = 9 \): \[ \frac{Y}{X} = \frac{9}{-6} = -1.5 \]
Since the ratio \( \frac{Y}{X} \) is constant at \(-1.5\) for all pairs, we can conclude that the relationship between X and Y is proportional.