1. The problem is to understand the relationship between cups of lemonade mix and cups of water. 2. Given the table: | Cups of Lemonade Mix | Cups of Water | |----------------------|---------------| | 2 | 5 | | 6 | 15 | | 8 | 20 | | 16 | 40 | 3. We want to find the formula that relates cups of lemonade mix ($x$) to cups of water ($y$). 4. From the table, observe the ratio $\frac{y}{x}$: $$\frac{5}{2} = 2.5, \quad \frac{15}{6} = 2.5, \quad \frac{20}{8} = 2.5, \quad \frac{40}{16} = 2.5$$ 5. Since the ratio is constant, the relationship is linear and can be expressed as: $$y = 2.5x$$ 6. This means for every cup of lemonade mix, you need 2.5 cups of water. 7. The given function $y = 2.5x$ perfectly models the data in the table. Final answer: $$y = 2.5x$$