1. The problem is to convert the inequality $10x + 32y \geq 5000$ into slope-intercept form. 2. The slope-intercept form for a line is given by the formula: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. To convert the inequality, first isolate $y$ on one side: $$10x + 32y \geq 5000$$ Subtract $10x$ from both sides: $$32y \geq 5000 - 10x$$ 4. Now divide every term by 32 to solve for $y$: $$y \geq \frac{5000}{32} - \frac{10}{32}x$$ 5. Simplify the fractions: $$y \geq 156.25 - 0.3125x$$ 6. Rewrite the inequality in slope-intercept form: $$y \geq -0.3125x + 156.25$$ This means the line has a slope of $-0.3125$ and a y-intercept of $156.25$, and the region above or on this line satisfies the inequality.