Questions: y varies inversely with x. y is 2 when x is 9. What is y when x is 6?

Solution Steps

To solve this problem, we need to use the concept of inverse variation. When two variables vary inversely, their product is constant. Given that \( y \) is 2 when \( x \) is 9, we can find the constant of variation. Then, we use this constant to find \( y \) when \( x \) is 6.

Given that \( y \) varies inversely with \( x \), we know that \( y \cdot x = k \), where \( k \) is a constant. We are given \( y = 2 \) when \( x = 9 \). Therefore, we can find \( k \) as follows: \[ k = y \cdot x = 2 \cdot 9 = 18 \]

We need to find \( y \) when \( x = 6 \). Using the constant of variation \( k = 18 \), we can set up the equation: \[ y \cdot 6 = 18 \] Solving for \( y \): \[ y = \frac{18}{6} = 3 \]

Final Answer