1. **State the problem:** We need to write an equation in slope-intercept form $y = mx + b$ that represents the monthly cost $y$ of the farm when it produces $x$ eggs. 2. **Identify the components:** - The cost per egg is $0.05$, so this is the slope $m$ because the cost increases by $0.05$ for each additional egg. - The fixed monthly upkeep cost is $1000$, which is the y-intercept $b$ because it is the cost when no eggs are produced. 3. **Write the equation:** $$y = 0.05x + 1000$$ 4. **Interpret the slope and intercept:** - Slope $m = 0.05$ means the cost increases by 5 cents per egg. - Intercept $b = 1000$ means the farm has a fixed monthly cost of 1000 regardless of egg production. 5. **Check the options:** - The first option matches our equation and interpretation. **Final answer:** The slope is $0.05$ because this is the cost per egg. The equation is $$y = 0.05x + 1000$$.