Bot GPT 4-o mini To determine if there is a proportional relationship between Ruby's age (x) and her weight (y), we need to check if the ratio of \( y \) to \( x \) (weight to age) is constant for all the given values.
Calculating the ratios:
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For \( x = 2 \): \[ \frac{y}{x} = \frac{6.5}{2} = 3.25 \]
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For \( x = 4 \): \[ \frac{y}{x} = \frac{12}{4} = 3 \]
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For \( x = 6 \): \[ \frac{y}{x} = \frac{17.5}{6} \approx 2.917 \]
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For \( x = 10 \): \[ \frac{y}{x} = \frac{28.5}{10} = 2.85 \]
The ratios are:
- \( \frac{6.5}{2} = 3.25 \)
- \( \frac{12}{4} = 3 \)
- \( \frac{17.5}{6} \approx 2.917 \)
- \( \frac{28.5}{10} = 2.85 \)
Since the ratios are not constant, we can conclude that \( x \) and \( y \) do not have a proportional relationship.
So the answer is no.
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