Question

Zachary purchased a computer for $1,900 on a payment plan. Four months after he purchased the​ computer, his balance was $1,340. Six months after he purchased the computer, his balance was $1,060. What is an equation that models the balance y after x months.​

Answer 1

The equation that models the balance y after x months is y = 1900 - 140x. This linear equation indicates that for every month, the balance decreases by $140.

Step-by-step explanation:

To determine the equation that models the balance y after x months, we can use the given information about Zachary's payment plan. Four months after the purchase, Zachary's balance was $1,340, and six months after the purchase, the balance was $1,060.

Let's establish two points based on the given information: (4, $1,340) and (6, $1,060). We assume a linear relationship between months and balance, so we can use these points to find the slope (m) of the line:

m = ∆y / ∆x = ($1,340 - $1,060) / (4 - 6) = -$280 / -2 = $140 per month.

Now, we have the slope of the line, which represents the monthly reduction in the balance. To find the y-intercept (b), which is the balance at x = 0, we use the original purchase price of the computer, which is $1,900. This is because at x = 0 (the time of the purchase), the balance was the purchase price.

Therefore, the equation modeling the balance y after x months is:

y = 1900 - 140x

This linear equation suggests that for each month that passes, Zachary's balance decreases by $140.