Bot GPT 4-o mini To find the constant of proportionality in the relationship between the number of pitchers of lemonade (x) and the number of lemons needed (y), we can express the relationship as \( y = kx \), where \( k \) is the constant of proportionality.
To find \( k \), we can use the given data points. We can calculate \( k \) using any of the provided pairs \((x, y)\):
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Using the pair \( (4, 28) \): \[ k = \frac{y}{x} = \frac{28}{4} = 7 \]
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Using the pair \( (7, 49) \): \[ k = \frac{49}{7} = 7 \]
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Using the pair \( (11, 77) \): \[ k = \frac{77}{11} = 7 \]
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Using the pair \( (12, 84) \): \[ k = \frac{84}{12} = 7 \]
In all cases, we find that the constant of proportionality \( k \) is 7.
Thus, the constant of proportionality is \( \boxed{7} \).
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