Budget line will shift in 2 cases:
1) Change in income of the consumer- If the income of the consumer increases then the budget line will shift to its right and if the income of the consumer decreases then the budget line will shift to its left.
2) Change in price of the commodity
(i) If price of both goods change then the budget line will shift to its left or right depending on the increase or decrease of the price of the good.
(ii) If the price of one good changes- If the price of one good changes while the other remains the same, then the budget line will shift parametrically, i.e, rotation of budget line (iii) If the price of one good increases and the price of other good decreases- If price of one good increases and the other good decreases, then the new budget line will intersect the old budget line.

In simple way... when change in technology and resources of both goods... known as shift
.....and if change in technology and resources of only one goods.... knows as... rotation

Shift and Rotation of Budget Line

Introduction
The budget line represents the different combinations of goods or services that an individual can afford given their income and the prices of the goods. It is a graphical representation of the budget constraint faced by consumers. The budget line can shift or rotate due to changes in income or prices of goods.

Shift of Budget Line
A shift in the budget line occurs when there is a change in income while prices of goods remain constant. There are two possible scenarios for the shift of the budget line:

1. Increase in Income: When there is an increase in income, the budget line shifts outward or to the right. This means that the individual can now afford more of both goods at any given price level. The slope of the budget line remains unchanged, indicating that the relative prices of the goods remain the same.

2. Decrease in Income: Conversely, when there is a decrease in income, the budget line shifts inward or to the left. This implies that the individual can afford less of both goods at any given price level. Again, the slope of the budget line remains constant, indicating that the relative prices of the goods remain unchanged.

Rotation of Budget Line
A rotation of the budget line occurs when there is a change in the prices of goods while income remains constant. There are two possible scenarios for the rotation of the budget line:

1. Increase in the Price of One Good: If the price of one good increases while the price of the other remains constant, the budget line rotates inward from the axis of the good with the increased price. This rotation indicates that the consumer can now afford less of the good with the increased price, given the constant income.

2. Decrease in the Price of One Good: Conversely, if the price of one good decreases while the price of the other remains constant, the budget line rotates outward from the axis of the good with the decreased price. This rotation signifies that the consumer can now afford more of the good with the decreased price, given the constant income.

Conclusion
Understanding the shift and rotation of the budget line is crucial in analyzing the impact of changes in income and prices on consumer choices. A shift in the budget line due to changes in income represents a change in the individual's purchasing power, while a rotation of the budget line due to changes in prices reflects the change in the relative affordability of goods. These changes help economists and policymakers assess the impact of various economic factors on consumer behavior and make informed decisions.