What is Budget Line
A budget line or budget constraint illustrates the alternative combinations of two different goods that can be purchased with a given income based on the prices of the two goods. Or budget line indicates the combination of commodities that a consumer can buy with a given income at a given set of prices. If the graph shows food and clothing, then each point on the line represents a combination of food and clothing that can be bought for a certain income level and with a given set of prices for the two goods.
The indifference curves portray the preferences of the consumer. If there were no constraints on his consumption behavior he will continuously move to a higher indifference curve since no consumer has unlimited resources to spend. Here is command to determine his behavior in the light of his limited financial resources.
It is seems that the consumer has a given income which sets limits to his maximize behavior. Income acts as a constraint in the attempt for maximizing utility. The income constraints in the case of two commodities may be written as:
M = P_{X} X + P_{y} Y
Where ‘X’ and ‘Y’ are two commodities prices of ‘x’ and ‘y’ are denote by P_{x} and P_{y} respectively or given ‘M’ is the consumer’s budget or disposable money income and is given fixed for the purchase of these two commodities ‘X’ and ‘Y’.
Since quantity of ‘Y’ is plotted on the vertical axis hence solving the equation we have
P_{x} X + P_{y} Y = M
Py Y = M – Px X
Y = M / P_{y} – P_{x} / P_{y} X
Lets assigning values to M, P_{x} and P_{y}
M = 8, Px = 2 and Py = 1
M = P_{x} X + P_{y} Y
8 = 2X + 1Y
For different qualities of x and y which can be purchased by the given income ‘M’ the relevant schedule is as follows
Combination 
Qt 
Qt 
P_{x} X + P_{y} Y = M 

X 
Y 

A 
0 
8 
2(0)+1(5) = 8 
B 
1 
6 
2(1)+1(6) = 8 
C 
2 
4 
2(2)+1(4) = 8 
D 
3 
2 
2(3)+1(2) = 8 
E 
4 
0 
2(4)+1(0) = 8 
Plotting these points (combinations) we get the budget line AE as shows in the following graph.
Explanation
The term 1/Py M shows the amount of ‘Y’ that can be purchased if X is not bought at all. This is the vertical intercept OA or 8/1 = 8 on the other hand the term 1/Px M shows that the quantity of X that can be purchased is Y is not bought. This is the horizontal intercept OE or 8/2 = 4.
The slope of the budget line or price line shows that how many units of Y the consumer will give up to purchase one more units of X with the given income prices of goods. In this case the slope of the budget line or budget constraint is OA / OE or 8/4 = 2/1 since the budget line is a straight line hence its slope is constant shift from any one point to any one point to any other point will yield the same value i.e. dy/dx = 2/1
Slope of the budget line or budget constraint is
Slope = dy/dx (M/P_{y} – P_{x} / P_{y} X)
= – P_{x} / P_{y}
Thus, slope of the budget line is negative price ratio. The budget line can be thus define as “different combination of two commodities which can be purchased with the help of given budget when the price of goods are known and fixed.