The variable y varies inversely with x. When x=6, y=9. What is the value of y when x=18?

Inverse variation means $xy$ is constant. From $x = 6$ and $y = 9$, the constant is 54. When $x = 18$, $y = \frac{54}{18} = 3$, choice D. Since $x$ tripled, $y$ must be divided by 3: $9 \div 3 = 3$. Choice A (27) multiplies by 3, treating the relationship as direct variation. Choice B (6) comes from subtracting 3, an additive rather than multiplicative change. Choice C (1.5) divides by 6, which would correspond to $x = 36$. Inverse variation always divides by the factor that multiplied $x$.