1. **State the problem:** Determine if $y$ varies directly with $x$ given the pairs $(-2,6)$, $(1,3)$, and $(4,8)$. If yes, write the direct variation equation in the form $y = kx$. 2. **Recall the direct variation rule:** If $y$ varies directly with $x$, then $y = kx$ for some constant $k$. 3. **Find $k$ for each pair:** - For $x = -2$, $y = 6$, so $k = \frac{y}{x} = \frac{6}{-2} = -3$. - For $x = 1$, $y = 3$, so $k = \frac{3}{1} = 3$. - For $x = 4$, $y = 8$, so $k = \frac{8}{4} = 2$. 4. **Check if $k$ is constant:** The values of $k$ are $-3$, $3$, and $2$, which are not equal. 5. **Conclusion:** Since $k$ is not constant, $y$ does not vary directly with $x$. **Final answer:** no