Final answer:
The statement is true; different prices for two goods result in different slopes of budget lines for two consumers, as the slope reflects the trade-off between the goods determined by their relative prices.
Step-by-step explanation:
The statement that if two consumers face different prices of two goods, then their budget lines will necessarily have different slopes is true. The slope of the budget line reflects the trade-off between the two goods, showing how much of one good a consumer can obtain by giving up some of the other good. This trade-off is determined by the relative prices of the two goods. If two consumers face different prices, the opportunity cost of one good in terms of the other varies, leading to different slopes for their budget constraints. The budget constraint is the boundary that represents the combination of goods that a consumer can purchase given their limited income and the prices of goods. Each point on the budget line indicates a combination where the total spending equals the consumer's budget. A change in the price of one good or both goods will pivot the budget line, altering its slope, but maintaining the consumer's income constant.