Which of the following is correct if x varies inversely with y?(1 point)%0D%0AResponses%0D%0A%0D%0AWhen x is multiplied by 4, y is multiplied by 4.%0D%0AWhen x is multiplied by 4, y is multiplied by 4.%0D%0A%0D%0AWhen x is multiplied by 4, y is divided by 4.%0D%0AWhen x is multiplied by 4, y is divided by 4.%0D%0A%0D%0AWhen x is increased by 4, y is decreased by 4.%0D%0AWhen x is increased by 4, y is decreased by 4.%0D%0A%0D%0AWhen x is divided by 4, y is divided by 4.

1 answer

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.