The budget line shows purchasing possibilities

Its intercepts and slope come from income and prices.

Every point on the line exhausts the budget, while points inside are affordable but leave income unspent and points outside are currently unaffordable.

With income I, prices P_X and P_Y, affordable bundles satisfy P_XX+P_YY≤ I. The horizontal intercept is I/P_X. The vertical intercept is I/P_Y. The slope is -P_X/P_Y, the market opportunity cost of one more unit of X in units of Y.

An intercept answers an all-or-nothing question. If income is $60, P_X=$6, and P_Y=$3, the consumer can buy at most 10 units of X or 20 units of Y. Bundles on the line exhaust the budget. Bundles inside are affordable and leave unspent income. Bundles outside are not affordable at the stated prices.

The budget equation is 6X+3Y=60. Solving for Y gives Y=20-2X, so the slope is -2. Each additional X requires giving up two Y because X costs twice as much. The slope records a market tradeoff set by relative prices, not the consumer’s preference.

Higher income shifts the line outward in parallel when prices are fixed. Lower income shifts it inward. A fall in P_X rotates the line outward around the unchanged Y-intercept. A simultaneous proportional increase in income and both prices leaves the budget set unchanged.

A price change alters both purchasing power and the relative price. If P_X falls, the consumer can buy more X with the same income, and X becomes cheaper in terms of Y. Those two effects later become the income and substitution effects. The rotation visually contains both.

Test a bundle before optimizing

Income is $48, notebooks cost $6, and meals cost $4. A bundle of 4 notebooks and 6 meals costs 4($6)+6($4)=$48, so it lies on the line. A bundle of 5 and 6 costs $54 and is unaffordable. Utility cannot make an outside bundle feasible. Preferences choose only among bundles inside the constraint.

Real purchasing power depends on income relative to prices. A 10 percent income increase paired with 10 percent increases in both prices leaves every maximum quantity unchanged. Nominal income rose, but the opportunity set did not. This prevents the common mistake of treating any dollar-income increase as an outward shift without checking prices.

The budget line states what can be purchased, not what should be purchased. To find the best bundle, combine it with marginal utility or indifference curves. A point on the line can be affordable but inferior to another affordable point. Feasibility comes first. Preference determines the selection within it.

When the inequality P_XX+P_YY≤ I is used, every point below the line belongs to the budget set. When drawing the line itself, use equality because it traces bundles that exhaust income. Confusing the budget set with its boundary can make an affordable interior bundle look impossible.

An outside point may be preferred, but preference cannot make it affordable under the stated income and prices.