1. **State the problem:** We are given inequalities involving $x$ and $y$: $$25x + 12.50y \geq 1000$$ $$x + y \leq 15000$$ We want to express these inequalities in slope-intercept form ($y = mx + b$) and understand the feasible region. 2. **Rewrite the first inequality:** Start with: $$25x + 12.50y \geq 1000$$ Subtract $25x$ from both sides: $$12.50y \geq 1000 - 25x$$ Divide both sides by $12.50$: $$y \geq \frac{1000 - 25x}{12.50}$$ Show cancellation: $$y \geq \frac{\cancel{1000} - \cancel{25}x}{\cancel{12.50}}$$ Simplify: $$y \geq 80 - 2x$$ 3. **Rewrite the second inequality:** Start with: $$x + y \leq 15000$$ Subtract $x$ from both sides: $$y \leq 15000 - x$$ 4. **Summary:** The inequalities in slope-intercept form are: $$y \geq -2x + 80$$ $$y \leq -x + 15000$$ 5. **Interpretation:** - The first inequality represents the region above or on the line $y = -2x + 80$. - The second inequality represents the region below or on the line $y = -x + 15000$. 6. **Final answer:** The system of inequalities is: $$\boxed{y \geq -2x + 80 \quad \text{and} \quad y \leq -x + 15000}$$ This describes the feasible region bounded by these two lines.