To determine which table represents a function that is proportional, we need to check if the relationship between \( x \) and \( y \) is such that \( y \) is directly proportional to \( x \). This means that the ratio \( \frac{y}{x} \) should be constant for all pairs of \( (x, y) \).
Let's analyze each function:
Function 1:
- For \( x = 1, y = 2 \): \( \frac{y}{x} = \frac{2}{1} = 2 \)
- For \( x = 2, y = 4 \): \( \frac{y}{x} = \frac{4}{2} = 2 \)
- For \( x = 3, y = 6 \): \( \frac{y}{x} = \frac{6}{3} = 2 \)
Since \( \frac{y}{x} = 2 \) for all values, Function 1 is proportional.
Function 2:
- For \( x = 1, y = 2 \): \( \frac{y}{x} = \frac{2}{1} = 2 \)
- For \( x = 2, y = 3 \): \( \frac{y}{x} = \frac{3}{2} = 1.5 \)
- For \( x = 3, y = 4 \): \( \frac{y}{x} = \frac{4}{3} \approx 1.33 \)
Since the ratios \( \frac{y}{x} \) are not constant (2, 1.5, and approximately 1.33), Function 2 is not proportional.
Conclusion: Function 1 represents a function that is proportional.
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