Bot GPT 4-o mini To find the constant of proportionality \( k \) in the relationship between the number of suits \( x \) and the total cost \( y \), we can use the formula:
\[ y = kx \]
We can use any of the provided pairs of \( (x, y) \) to find \( k \).
Let's use the first pair \( (1, 8) \):
\[ 8 = k \cdot 1 \implies k = 8 \]
Now, let's verify this with the other pairs:
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For \( x = 6 \): \[ y = 8 \cdot 6 = 48 \quad \text{(which matches)} \]
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For \( x = 7 \): \[ y = 8 \cdot 7 = 56 \quad \text{(which matches)} \]
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For \( x = 9 \): \[ y = 8 \cdot 9 = 72 \quad \text{(which matches)} \]
All pairs confirm that the constant of proportionality \( k \) is indeed:
\[ \boxed{8} \]
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