The variable y varies directly with x. When x=6, y=18. What is the value of y when x=15?

Direct variation means $y = kx$ for a constant $k$. From $x = 6$ and $y = 18$, $k = \frac{18}{6} = 3$. When $x = 15$, $y = 3 \times 15 = 45$. Check by proportion: $x$ grows by a factor of $\frac{15}{6} = 2.5$, so $y$ grows by the same factor, $18 \times 2.5 = 45$. A common wrong answer is 7.2, which comes from treating the relationship as inverse and computing $\frac{6 \times 18}{15}$. Another is 27, from adding the change in $x$ (9) to $y$ instead of scaling. Direct variation multiplies; it does not add.