A proportional relationship can be identified by the equation having the form \( y = kx \), where \( k \) is a constant. This means that when \( x \) is 0, \( y \) must also equal 0, which indicates that the graph passes through the origin (0,0).
Now, let's analyze the given equations:
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\( y = 3x + 1 \): This is not proportional because it does not pass through the origin. When \( x = 0 \), \( y = 1 \).
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\( y = \frac{1}{3} x \): This is a proportional relationship since it can be rewritten as \( y = kx \) with \( k = \frac{1}{3} \). It passes through the origin.
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\( y = x^3 - 3 \): This is not proportional because it does not pass through the origin. When \( x = 0 \), \( y = -3 \).
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\( y = x + 3 \): This is not proportional because it does not pass through the origin. When \( x = 0 \), \( y = 3 \).
Based on the analysis above, the equation that represents a proportional relationship is:
\( y = \frac{1}{3} x \).