Question

Zachary purchased a computer for $2,700 on a payment plan. Two months after he purchased the computer, his balance was $2,250. Five months after he purchased the computer, his balance was $1,575. What is an equation that models the balance y after x months?

Answer 1

To find the equation that models the balance after x months, we calculate the monthly decrease and apply it to the initial balance to get the equation y = 2700 - 225x.

Step-by-step explanation:

The question requires us to find an equation that models the balance, y, after x months for a computer purchased on a payment plan. Given the initial purchase price of $2,700, a balance of $2,250 after two months, and $1,575 after five months, we can determine the monthly rate of decrease using two points: (2, 2250) and (5, 1575).

We calculate the monthly rate of decrease as:

(Balance at 2 months - Balance at 5 months) / (Month 5 - Month 2)

(2250 - 1575) / (5 - 2) = 675 / 3 = $225 per month

Using the point-slope form of a linear equation, we can write an equation that represents the balance after x months since the computer was purchased. Starting from the initial condition:

y = initial balance - (monthly decrease × months after purchase)

y = 2700 - 225x

This equation assumes that the payment plan has a fixed monthly payment.