\( y \) varies directly with \( x \). \( y \) is 12 when \( x \) is 4 . What is \( x \) when \( y \) is \( 9 ? \) \( x=[?] \)

To find the direct variation between \( y \) and \( x \), we can establish the relationship \( y = kx \), where \( k \) is the constant of proportionality. From the information given, when \( y = 12 \), \( x = 4 \). We can calculate \( k \) as follows: \[ k = \frac{y}{x} = \frac{12}{4} = 3 \] Now we can rewrite the equation as \( y = 3x \). Next, we need to find \( x \) when \( y \) is \( 9 \): \[ 9 = 3x \] Dividing both sides by 3, we get: \[ x = \frac{9}{3} = 3 \] So, \( x = 3 \).