Question

Zachary purchased a computer for $1,900 on a payment plan. two months after he purchased the computer, his balance was $1,660. nine months after he purchased the computer, his balance was $820. what is an equation that models the balance b after m months?

Answer 1

To model the balance of Zachary's computer after m months, we can use a linear equation. The equation is b = -20m + 1700, where b is the balance and m is the number of months.

Step-by-step explanation:

To find an equation that models the balance of Zachary's computer after m months, we can use the given information to form a linear equation. Let x represent the number of months after the computer was purchased. The initial balance is $1,900, and after 2 months ($x = 2), the balance is $1,660. After 9 months ($x = 9), the balance is $820. We can set up two points: (2, 1660) and (9, 820).

Using the slope-intercept form, y = mx + b, where y is the balance and x is the number of months:

First, find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1) = (820 - 1660) / (9 - 2) = -140 / 7 = -20.

Next, substitute the slope and one of the points into the equation: 1660 = -20(2) + b.

Now, solve for b: b = 1660 + 40 = 1700.

The equation that models the balance (b) after m months is: b = -20m + 1700.