Question

Elani signed up for an installment plan with 0% interest to purchase a new couch that costs $770. She creates an equation to model the situation, where x represents the number of months and y represents the balance of the installment account: y = 770 − 55x. Determine the missing steps and justifications in the solution.

Answer 1

The equation y = 770 - 55x models the balance of Elani's installment account, with 770 being the initial balance and -55 the monthly payment. It takes 14 months to pay off the couch. The y-intercept and the slope represent the starting balance and the rate of payment, respectively.

Step-by-step explanation:

The equation y = 770 - 55x represents the balance of the installment account for the purchase of a new couch. The independent variable is x, which stands for the number of months, and the dependent variable y represents the remaining balance of the account. To determine the monthly payment and the duration of the payment plan, we can solve for x when y is equal to zero:

• Set the equation to zero: 0 = 770 - 55x.
• Solve for x: x = 770 / 55.
• Calculate x: x = 14.

This means that it will take Elani 14 months to pay off the couch in full, with equal monthly payments of $55.

In this scenario, the y-intercept is 770, which signifies the initial balance owed for the couch. The slope of the line, -55, represents the rate at which the balance decreases each month as Elani makes the payments.