A proportional relationship is one where two variables vary directly with each other, typically represented by the equation \( y = kx \), where \( k \) is a constant.
Let's analyze each of the given equations:
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\( y = x^3 - 3 \): This is not proportional because it includes a cubic term and a constant, which means it will not pass through the origin.
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\( y = \frac{x}{3} - 3 \): This is not proportional because of the constant term \(-3\).
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\( y = 3x + 1 \): This is not proportional because of the constant term \(+1\).
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\( y = x + 3 \): This is not proportional because of the constant term \(+3\).
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\( y = 13x \): This equation represents a proportional relationship since it follows the form \( y = kx \) with \( k = 13\).
Thus, the correct answer is:
\( y = 13x \)