In a direct variation, the relationship between \( x \) and \( f(x) \) can be expressed as:
\[ f(x) = kx \]
where \( k \) is the constant of variation.
To find \( k \), we can use the provided pairs \((x, f(x))\) where \( f(x) \) is not zero:
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For the pair \( (3, 6) \): \[ 6 = k \cdot 3 \implies k = \frac{6}{3} = 2 \]
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For the pair \( (4, 8) \): \[ 8 = k \cdot 4 \implies k = \frac{8}{4} = 2 \]
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For the pair \( (7, 14) \): \[ 14 = k \cdot 7 \implies k = \frac{14}{7} = 2 \]
In all cases, we find that:
\[ k = 2 \]
Thus, the constant of variation \( k \) is \( 2 \).