f \( y \) varies directly with \( x \) and \( y=6 \) when \( x=3 \), find \( y \) when \( x=2 \). Write and solve a direct variation equation to find the answer. \( y=\square \) Submit

To solve the direct variation problem, follow these steps: ### 1. **Understand Direct Variation** When \( y \) varies directly with \( x \), it means that \( y \) is equal to a constant multiplied by \( x \). This relationship can be expressed as: \[ y = kx \] Where: - \( k \) is the constant of variation. ### 2. **Find the Constant of Variation (\( k \))** You're given that \( y = 6 \) when \( x = 3 \). Plug these values into the equation to find \( k \): \[ 6 = k \times 3 \] Solving for \( k \): \[ k = \frac{6}{3} = 2 \] ### 3. **Write the Direct Variation Equation** Now that you have the value of \( k \), substitute it back into the direct variation equation: \[ y = 2x \] \[ \boxed{y = 2x} \] ### 4. **Find \( y \) When \( x = 2 \)** Use the direct variation equation to find \( y \) when \( x = 2 \): \[ y = 2 \times 2 = 4 \] \[ \boxed{y = 4} \] ### **Summary** - **Direct Variation Equation:** \( y = 2x \) - **When \( x = 2 \):** \( y = 4 \)