Final answer:
The budget constraint with a $450 budget for textbooks costing $55 each and CDs costing $12 each is given by the equation y = -4.58x + 37.5, where x is the number of textbooks and y is the number of CDs.
Step-by-step explanation:
To calculate the budget constraint for the scenario of textbooks and CDs with a monthly budget of $450, let x represent the number of textbooks and y represent the number of CDs. The average cost of a textbook is $55, and the cost of a CD is $12. The total spending on textbooks and CDs cannot exceed the budget, so the equation representing this constraint is 55x + 12y = 450.
To rewrite the constraint in the form y=mx+b, we need to solve for y. This gives us: y = (-55/12)x + (450/12), which simplifies to y = -4.58x + 37.5. Here, m is the slope of the budget line (-4.58), showing the trade-off between textbooks and CDs, while b is the y-intercept (37.5) representing the maximum number of CDs that could be bought if no textbooks are purchased.
The correct budget constraint equation is y = -4.58x + 37.5.