If \( x \) varies inversely with \( y \), it means that the product of \( x \) and \( y \) is constant. Mathematically, this can be expressed as:
\[ x \cdot y = k \]
for some constant \( k \).
From this relationship, if \( x \) is multiplied by 4, the new value of \( x \) becomes \( 4x \). To maintain the constant \( k \):
\[ 4x \cdot y' = k \]
Since \( x \cdot y = k \), we can substitute \( k \) with \( x \cdot y \):
\[ 4x \cdot y' = x \cdot y \]
Dividing both sides by \( 4x \) gives:
\[ y' = \frac{y}{4} \]
This means that when \( x \) is multiplied by 4, \( y \) is divided by 4.
Thus, the correct statement is:
When x is multiplied by 4, y is divided by 4.
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