A shift in the budget line, when prices are constant, is due to.

Option 1 -> Change in demand affects the consumer's choice but does not shift the budget line itself.

Option 2 -> Change in income shifts the budget line parallel (outward if income increases, inward if income decreases) while keeping the slope unchanged.

Option 3 -> Change in preferences affects indifference curves, not the budget line.

Option 4 -> Change in utility is reflected in indifference curves, not the budget line.

Hence, Option 2: Change in the income of the consumer -> The budget line represents all combinations of goods a consumer can afford given their income and market prices. The equation is M = P₁X₁ + P₂X₂. When prices remain constant but income (M) changes, the budget line shifts parallel to itself - outward for an increase in income and inward for a decrease. The slope of the budget line (−P₁/P₂) remains the same because it depends only on prices, which are held constant. -> correct