The budget line is a negatively downward sloping line. The slope of a budget line measures the amount of good 2 that must be sacrificed in order to get an additional unit of good 1, as the consumerâ€s income (M) is fixed. The budget line is downward sloping because, in order to increase the consumption of one good, the consumption of the other good must be reduced, with constant M.
The slope of the budget line is \\(\\frac{-P_{1}}{P_{2}}=\\frac{\\Delta x_{2}}{\\Delta x_{1}}\\), which implies the rate of exchange or the rate at which good 2 can be substituted for good 1.