Final answer:
The balance of a student's payment plan for a computer can be expressed as a linear equation B(M) = -150M + 1800, where M is the number of months and B is the balance. The slope of -150 represents the monthly reduction in balance.
Step-by-step explanation:
Given that a student purchased a computer on a payment plan and the balance after certain months, we can model this situation with a linear equation. We're provided with two key pieces of data: three months after purchase, the balance was $1,350, and five months after purchase, the balance was $1,050. We can calculate the rate of change, which is the slope of our equation, by taking the difference in balance and dividing it by the difference in time:
\((1350 - 1050) \div (5 - 3) = 300 \div 2 = 150\)
The slope of the payment plan is -$150 per month. We can use one of the points to find the y-intercept, which represents the balance at month 0. Let's use the point (3, $1,350).
\(1350 = -150(3) + b\)
\(b = 1350 + 450\)
\(b = 1800\)
The y-intercept, $1,800, is the initial balance. Now, we have our slope and our y-intercept, so our equation will be:
\(B(M) = -150M + 1800\)
The slope, in this case, represents the monthly decrease in the balance, meaning $150 is paid toward the balance each month. This equation models the balance B after M months.