To find the equation of the line \( y = mx \) that describes the proportional relationship given by the points (1, 3), (2, 6), and (3, 9), we need to determine the slope \( m \).
Since the relationship is proportional, we can calculate \( m \) using any of the points. The slope \( m \) is defined as:
\[ m = \frac{y}{x} \]
Using the points provided:
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Using the point (1, 3): \[ m = \frac{3}{1} = 3 \]
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Using the point (2, 6): \[ m = \frac{6}{2} = 3 \]
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Using the point (3, 9): \[ m = \frac{9}{3} = 3 \]
In each case, we find that \( m = 3 \).
Thus, the equation of the line that describes the proportional relationship is:
\[ y = 3x \]