A shift in income, holding everything else constant, will ...

A. shift the budget constraint in a parallel fashion.

B. will shift and rotate the budget constraint

C. will rotate the budget constraint

A. shift the budget constraint in a parallel fashion.

Explanation:

Budget Line / Constraint is graphical representation of product combinations that a consumer can buy, given product prices & income (all spent).

Income change will lead to parallel shift in budget constraint, because of equivalent proportional change in purchasing power of both goods.

If Income increases: the consumer can increase consumption of both goods with risen income, because of increased real income / purchasing power due to price fall. This will shift budget constraint rightwards / outwards.

Similarly: Income decrease would decrease real income / purchasing power for both the goods, enabling less consumption of both. This will shift budget constraint leftwards / inwards.

Both options B & C are inapt because : Budget Line Rotation occurs in case of price & purchasing power change only in one good or disproportionately in two goods.