The intercepts of this budget constraint on each axis equals income divided by the price of the good represented on the axis. This can be demonstrated quite easily using basic algebra as follows:

X = 1/Px – (Py/Px)Y

In Equation, the first term on the right is the intercept of the line on the horizontal axis: it is the amount of good X that could be bought by the consumer if he or she spent all his or her income on good X. In other words, if the consumer expends all her or his income just for good X, Equation provides the answer. Similar logic is supposed to apply for the maximum consumed amount of good Y, as well. Or, if the consumer spends all his or her income just for consuming good Y, intersection on Y axis will be equal to I/Py. When we combine these two intersection points on both axis, we find the budget line or constraint and its slope is equal to the negative of price ratios, Px/Py which is the result of (I/Py)/(I/Px). Thus, the slope equals the relative price of the two goods, that is, the price of one good compared to the price of the other.