Which of the following is correct if x varies inversely with y?(1 point)

Question

Responses

When x is divided by 4, y is divided by 4.
When x is divided by 4, y is divided by 4.

When x is multiplied by 4, y is divided by 4.
When x is multiplied by 4, y is divided by 4.

When x is multiplied by 4, y is multiplied by 4.
When x is multiplied by 4, y is multiplied by 4.

When x is increased by 4, y is decreased by 4.

Answer 1

If \( x \) varies inversely with \( y \), it can be expressed mathematically as \( x \cdot y = k \), where \( k \) is a constant. This means that as one variable increases, the other variable must decrease in order to keep the product \( k \) constant.

Let's evaluate the options provided:

1. When x is divided by 4, y is divided by 4.

   • Incorrect. If \( x \) is divided by 4, then \( y \) must be multiplied by 4 to keep the product constant.

2. When x is multiplied by 4, y is divided by 4.

   • Correct. Multiplying \( x \) by 4 will cause \( y \) to decrease by a factor of 4 in order to keep the product \( k \) constant.

3. When x is multiplied by 4, y is multiplied by 4.

   • Incorrect. This would contradict the relationship of inverse variation.

4. When x is increased by 4, y is decreased by 4.

   • Incorrect. The specific values of increase and decrease do not hold for inverse variation; it's about the proportional relationship rather than specific addition or subtraction.

So, the correct statement is: When x is multiplied by 4, y is divided by 4.