1. **State the problem:** Jacques has a weekly budget of 24 to spend on candy bars and eggs. Candy bars cost 2 per pack, eggs cost 6 per dozen. We want to find how many packs of candy bars or dozens of eggs he can buy if he spends all his money on one good. 2. **Write the budget constraint equation:** Let $x$ be the number of candy bar packs and $y$ be the number of egg dozens. The total cost must equal the budget: $$2x + 6y = 24$$ 3. **Find intercepts:** - If Jacques spends all money on candy bars ($y=0$): $$2x = 24 \implies x = \frac{24}{2} = 12$$ - If Jacques spends all money on eggs ($x=0$): $$6y = 24 \implies y = \frac{24}{6} = 4$$ 4. **Rewrite the budget line in slope-intercept form:** $$6y = 24 - 2x \implies y = 4 - \frac{1}{3}x$$ 5. **Interpret the slope:** The slope is $-\frac{1}{3}$, meaning for each additional pack of candy bars Jacques buys, he must buy one-third fewer dozens of eggs to stay within budget. 6. **Summary:** - Maximum candy bars if no eggs: 12 packs - Maximum eggs if no candy bars: 4 dozens - Budget line equation: $$y = 4 - \frac{1}{3}x$$ - Slope: $-\frac{1}{3}$, showing the trade-off rate between candy bars and eggs.