1. **State the problem:** Determine whether $x$ and $y$ show direct variation, inverse variation, or neither for equations 4 to 11. 2. **Recall definitions:** - Direct variation: $y = kx$ for some constant $k$. - Inverse variation: $xy = k$ or $y = \frac{k}{x}$ for some constant $k$. - Neither: relationship does not fit either form. 3. **Analyze each equation:** **4.** $y = 5x$ - This is exactly $y = kx$ with $k=5$, so direct variation. **5.** $y = \frac{7}{x}$ - This is $y = \frac{k}{x}$ with $k=7$, so inverse variation. **6.** $xy = -4$ - Matches $xy = k$ with $k=-4$, inverse variation. **7.** $y = x^2$ - Not linear in $x$, so neither. **8.** $y = 3x + 2$ - Has an added constant, not pure $y = kx$, so neither. **9.** $x = \frac{1}{y}$ - Rearranged: $xy = 1$, inverse variation. **10.** $y = -2x$ - Matches $y = kx$ with $k=-2$, direct variation. **11.** $y = 4$ - Constant $y$, no $x$ dependence, neither. 4. **Final answers:** - 4: direct variation - 5: inverse variation - 6: inverse variation - 7: neither - 8: neither - 9: inverse variation - 10: direct variation - 11: neither