If $y$ varies directly as $x$ , and $y=18$ when $x=6$ , find $y$ when $x=10$.

• A. $3$
• B. $30$
• C. $60$
• D. $9$

Answer: (B)

Verified step by step guidance

1. Understand that if \( y \) varies directly as \( x \), it means there is a constant \( k \) such that \( y = kx \).
2. Use the given values \( y = 18 \) when \( x = 6 \) to find the constant of proportionality \( k \) by substituting into the equation: \( 18 = k \times 6 \).
3. Solve for \( k \) by dividing both sides of the equation by 6: \( k = \frac{18}{6} \).
4. Write the direct variation equation with the found constant \( k \): \( y = kx \).
5. Use the equation to find \( y \) when \( x = 10 \) by substituting 10 for \( x \): \( y = k \times 10 \).