To determine the constant of proportionality for the ratio of pancake mix to milk, let's follow these steps:
1. Identify the quantities given for milk and pancake mix:
- Hector used 6 cups of milk.
- Hector used 9 cups of pancake mix.
2. Set up the ratio of pancake mix to milk:
- This can be represented as the fraction [tex]\(\frac{\text{pancake mix}}{\text{milk}}\)[/tex].
- Substituting the given values, the ratio is [tex]\(\frac{9 \text{ cups of pancake mix}}{6 \text{ cups of milk}}\)[/tex].
3. Simplify the fraction:
- We simplify [tex]\(\frac{9}{6}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
- [tex]\(\frac{9 \div 3}{6 \div 3} = \frac{3}{2}\)[/tex].
4. Conclusion:
- The constant of proportionality for the ratio of pancake mix to milk is [tex]\(\frac{3}{2}\)[/tex].
Thus, the correct answer is [tex]\(\frac{3}{2}\)[/tex].
