1. **State the problem:** We want to find the slope of the budget constraint line for Jacques' spending on candy bars and eggs. 2. **Recall the budget line equation:** From previous work, the budget line is given by: $$y = 4 - \frac{1}{3}x$$ 3. **Identify the slope:** The slope is the coefficient of $x$ in the equation, which is: $$-\frac{1}{3}$$ 4. **Interpret the slope:** This means that for every additional pack of candy bars Jacques buys, he must buy $\frac{1}{3}$ fewer dozens of eggs to stay within his budget. 5. **Final answer:** The slope of the budget constraint is $-\frac{1}{3}$.