If \( y \) varies inversely with \( x \), we can express this relationship using the equation:
\[ y = \frac{k}{x} \]
where \( k \) is a constant.
Given that \( y = 4 \) when \( x = 7 \), we can substitute these values into the equation to find \( k \):
\[ 4 = \frac{k}{7} \]
To solve for \( k \), we multiply both sides by 7:
\[ k = 4 \times 7 = 28 \]
Now that we have the value of \( k \), we can write the equation for the inverse variation:
\[ y = \frac{28}{x} \]
This is the equation representing the inverse variation of \( y \) with respect to \( x \).