Since \(y\) varies inversely with \(x\), we can express this relationship with the equation:
\[ y = \frac{k}{x} \]
where \(k\) is a constant.
To find the value of \(k\), we can use the values given: \(y = 4\) when \(x = 6\).
Plugging in those values into the equation:
\[ 4 = \frac{k}{6} \]
To solve for \(k\), we can multiply both sides by 6:
\[ k = 4 \times 6 = 24 \]
Now that we have the value of \(k\), we can write the equation for the inverse variation:
\[ y = \frac{24}{x} \]
Thus, the equation for the inverse variation is:
\[ y = \frac{24}{x} \]
1 answer