Bot GPT 4-o mini To find the constant of proportionality in the relationship between the time (in days) spent making porch swings (x) and the number of swings built (y), we can express this relationship as a ratio \( \frac{y}{x} \).
From the given data:
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For \( x = 5 \) days, \( y = 1 \) swing: \[ \frac{y}{x} = \frac{1}{5} = 0.2 \]
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For \( x = 10 \) days, \( y = 2 \) swings: \[ \frac{y}{x} = \frac{2}{10} = 0.2 \]
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For \( x = 15 \) days, \( y = 3 \) swings: \[ \frac{y}{x} = \frac{3}{15} = 0.2 \]
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For \( x = 20 \) days, \( y = 4 \) swings: \[ \frac{y}{x} = \frac{4}{20} = 0.2 \]
In each case, the ratio \( \frac{y}{x} \) is consistently \( 0.2 \).
Therefore, the constant of proportionality is \( \boxed{0.2} \).
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