Bot GPT 4-o mini In a proportional relationship, the ratio of the total cost \( y \) to the number of items \( x \) remains constant.
From the information provided, we can determine the constant of proportionality by examining the relationship using any pair of values from the table.
Let's take the first pair:
- For 10 cookies, the cost is $10.
Calculating the ratio: \[ \text{Constant of proportionality} = \frac{y}{x} = \frac{10}{10} = 1 \]
Next, we can verify this with other pairs:
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For 11 cookies, the cost is $11: \[ \frac{11}{11} = 1 \]
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For 17 cookies, the cost is $17: \[ \frac{17}{17} = 1 \]
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For 19 cookies, the cost is $19: \[ \frac{19}{19} = 1 \]
In each case, the total cost divided by the number of cookies equals 1.
Thus, the constant of proportionality is \( \boxed{1} \).
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