\( y \) varies directly with \( x \) \( y \) is 16 when \( x \) is 4 . What is \( x \) when \( y \) is 36 ? \[ x=[?] \]

To find the relationship between \( y \) and \( x \), we can express it as \( y = kx \), where \( k \) is the constant of variation. Given \( y = 16 \) when \( x = 4 \), we can find \( k \): \[ k = \frac{y}{x} = \frac{16}{4} = 4. \] Now, we want to find \( x \) when \( y = 36 \): \[ 36 = 4x \implies x = \frac{36}{4} = 9. \] So, the value of \( x \) when \( y \) is 36 is: \[ x = 9. \]