1. **State the problem:** Dominique can spend up to 20 dollars on drinks for the dance squad. A bottle of water costs 0.80 and a sports drink costs 1.25. We need to write inequalities representing the spending limit in both slope-intercept and standard form, where $x$ is the number of water bottles and $y$ is the number of sports drinks. 2. **Define variables:** - $x$: number of water bottles - $y$: number of sports drinks 3. **Write the inequality for total cost:** The total cost is $0.80x + 1.25y$ and it must be less than or equal to 20: $$0.80x + 1.25y \leq 20$$ 4. **Convert to slope-intercept form:** Solve for $y$: $$1.25y \leq 20 - 0.80x$$ $$y \leq \frac{20 - 0.80x}{1.25}$$ Simplify the fractions: $$y \leq 16 - 0.64x$$ 5. **Convert to standard form with integers:** Multiply both sides of the original inequality by 100 to clear decimals: $$80x + 125y \leq 2000$$ Divide by 5 to simplify: $$16x + 25y \leq 400$$ 6. **Interpretation:** - The slope-intercept form $y \leq 16 - 0.64x$ shows the maximum sports drinks $y$ Dominique can buy given $x$ water bottles. - The standard form $16x + 25y \leq 400$ represents the same constraint with integer coefficients. **Final answers:** - Slope-intercept form: $$y \leq 16 - 0.64x$$ - Standard form: $$16x + 25y \leq 400$$