Question

Zachary purchased a computer for $1,700 on a payment plan. two months after he purchased the computer, his balance was $1,470. twelve months after he purchased the computer, his balance was $320. what is an equation that models the balance y after x months?

Answer 1

An equation that models the balance y after x months for Zachary's computer purchase is:

y = -115x + 1,700

Step-by-step explanation:

The given information provides two data points: at two months ( x = 2 ), the balance is $1,470, and at twelve months (x = 12), the balance is $320. Using these points, we can construct a linear equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

First, determine the slope (m):

`\[ m = \frac{{\text{{change in }} y}}{{\text{{change in }} x}} = \frac{{320 - 1,470}}{{12 - 2}} = -115 \]`

Now that we have the slope (m), substitute it and one of the data points (let's use x = 2, y = 1,470) into the slope-intercept form:

`\[ 1,470 = -115 * 2 + b \]`

Solving for b:

b = 1,700

Thus, the equation that models the balance y after x months is y = -115x + 1,700. This equation allows us to predict the remaining balance (y) after any given number of months (x).