1. **State the problem:** Determine whether $x$ and $y$ show direct variation, inverse variation, or neither for the equations given. 2. **Recall definitions:** - Direct variation means $y = kx$ for some constant $k$. - Inverse variation means $xy = k$ or $y = \frac{k}{x}$ for some constant $k$. - Neither means the relationship does not fit either form. 3. **Analyze each equation:** **For 1.** $xy = 3$ - This matches the form $xy = k$ with $k=3$, so it is inverse variation. **For 2.** $x + y = 12$ - This cannot be written as $y = kx$ or $y = \frac{k}{x}$, so it is neither. **For 3.** $\frac{y}{x} = 6$ - Multiply both sides by $x$: $$y = 6x$$ - This matches $y = kx$ with $k=6$, so it is direct variation. 4. **Final answers:** - 1: inverse variation (T) - 2: neither (H) - 3: direct variation (E)