Since \( y \) varies inversely with \( x \), we can express this relationship using the equation:
\[ y = \frac{k}{x} \]
where \( k \) is a constant.
To find the value of \( k \), we can use the given information: \( y = 4 \) when \( x = 6 \).
Substituting these values into the equation gives:
\[ 4 = \frac{k}{6} \]
To solve for \( k \), we can multiply both sides by 6:
\[ k = 4 \cdot 6 = 24 \]
Now that we have found \( k \), we can write the equation for the inverse variation:
\[ y = \frac{24}{x} \]
This is the equation that represents the inverse variation between \( y \) and \( x \).
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