An increase in the price of good $x$ and an increase in the price of good $y$ may or may not change the slope of the budget constraint.

Question

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The slope of the budget constraint changes only if the prices of two goods change proportionally. If the prices of both goods increase or decrease by the same proportion, then the slope remains the same, and the budget constraint simply shifts inwards or outwards depending on the direction of the price change. If the prices of the two goods change by different proportions, then the slope of the budget constraint will change. If the two goods are complements, meaning that they are typically consumed together, then an increase in the price of one of them would lead to a decrease in the quantity demanded of both goods, resulting in a steeper slope of the budget constraint. On the other hand, if the two goods are substitutes, meaning that they can be used in place of each other, then an increase in the price of one of them would result in an increase in the quantity demanded of the other, resulting in a flatter slope of the budget constraint. In general, it depends on the nature of the goods and their relationship with each other.

An Increase in the Price of Good xxx And an Increase in the Price of Good

An Increase in the Price of Good $x$ And an Increase in the Price of Good