1. **State the problem:** We know that $y$ varies inversely as $x$, which means $y = \frac{k}{x}$ for some constant $k$. Given $y=8$ when $x=3$, find the constant $k$. Then find $x$ when $y=1.2$. Finally, create a variation table for given $x$ values. 2. **Formula and explanation:** In inverse variation, the product $xy$ is constant, so $xy = k$. This means as $x$ increases, $y$ decreases proportionally. 3. **Find the constant $k$:** Using $y=8$ and $x=3$, substitute into $xy=k$: $$k = 3 \times 8 = 24$$ 4. **Find $x$ when $y=1.2$:** Using $xy = 24$, substitute $y=1.2$: $$x = \frac{24}{1.2} = 20$$ 5. **Variation table:** For selected $x$ values, calculate $y = \frac{24}{x}$. | $x$ | $y = \frac{24}{x}$ | |-----|------------------| | 1 | 24 | | 2 | 12 | | 3 | 8 | | 4 | 6 | | 6 | 4 | | 8 | 3 | | 12 | 2 | | 24 | 1 | This table shows how $y$ decreases as $x$ increases, consistent with inverse variation. **Final answers:** - Constant of variation $k = 24$ - When $y=1.2$, $x=20$