The slope of the budget constraint represents the rate at which a consumer can trade one product for another. For example, a student spends his weekly allowance of $100 on purchasing books and snacks. A book costs $20 and a snack costs $5. Earlier, the student bought three books and eight snacks. Now, he buys four books and four snacks. In doing so, the student trades four snacks for one book. This gives us a slope of four snacks for one book.

The slope of the budget constraint is determined by the relative prices of the two products. If the student wants to buy more books and stay within his budget, he has to buy fewer snacks. For instance, in buying one more book costing $20, he must give up four snacks priced at $5 each. This is because the relative price of books in terms of snacks is 4, or $20/$5.

For two goods X and Y, the slope of budget constraint is given as:

Slope of budget constraint = -(P_x/P_y)

Where,

P_x is the price of product X

P_y is the price of product Y