Budget line

$P_1 x_1+P_2 x_2=M$

Then slope of the budget line is___________.

$-\frac{P_1}{P_2}$

$P_1 x_1+P_2 x_2=M$

The set of bundles available to the consumer is called the budget set. The budget set is thus the collection of all bundles that the consumer can buy with her income at the prevailing market prices. Lets assume there are two goods in a bundle-bananas and mangoes.

Quantity of bananas is measured along the horizontal axis and quantity of mangoes is measured along the vertical axis. Any point in the diagram (as given below) represents a bundle of the two goods. All bundles in the positive quadrant which are on or below the line are included in the budget set. The budget set consists of all points on or below the straight line having the equation:

$P_1 x_1+P_2 x_2=M$

The line consists of all bundles which cost exactly equal to M. This line is called the budget line. Points below the budget line represent bundles which cost strictly less than M.

The budget line is a straight line with horizontal intercept $\frac{M}{P_1}$ and vertical intercept $\frac{M}{P_2}$ . The horizontal intercept represents the bundle that the consumer can buy if she spends her entire income on bananas. Similarly, the vertical intercept represents the bundle that the consumer can buy if she spends her entire income on mangoes.

The slope of the budget line is the is the ratio of the prices of good 1 and good 2. This would mean price of good on the x axis ($P_1$) divided price of goods on the y axis ($P_2$). The slope of a budget line is always negative as it is downward sloping.

Thus, in the present case, the slope of the budget line is $-\frac{P_1}{P_2}$.