Final answer:
The slope of the budget constraint line in economics is the negative of the ratio of the prices of two goods (Px/Py), indicating that as more of one good is consumed, less of the other must be given up due to limited income.
Step-by-step explanation:
The slope of the budget constraint line is important in understanding how consumers make choices when faced with different prices and a limited income. In economics, the slope of the budget constraint is the negative of the ratio of the prices of two goods (Px/Py). This is because the budget constraint line represents all the combinations of two goods that a consumer can purchase given their income and the prices of the goods. When the price of one good (say, on the horizontal axis) goes up or down, the amount of that good that can be bought with a given budget changes, which is reflected in the slope of the budget line.
In the context of the question, the correct answer is b) the negative of the ratio of the prices (Px/Py). The slope is negative because as you consume more of one good, you must consume less of the other good due to the limited budget. The budget line, therefore, slopes downwards from left to right. Understanding this concept is critical for analyzing the substitution effect and the income effect in consumer choice theory, especially when looking at how changes in relative prices influence consumer's utility and buying power.