The slope of the budget line represents the amount of good "y" the consumer must give up to purchase one more unit of a good "x." The budget line itself represents the number of good bundles a consumer can buy with limited income.
If the prices of goods x and y remain the same, while the income to be spent on both decreases or increases, the slope of the budget line remains unchanged. A consumer must still give up the same amount of good y for one unit of good x, but the total number of good bundles that can be purchased decreases or increases respectively. The slope changes if the prices of goods change.