Question

Zachary purchased a computer for $1,300 on a payment plan. Two months after he purchased the computer, his balance was $1,090. Seven months after he purchased the computer, his balance was $565. What is an equation that models the balance y after x months?

The equation ______ models the balance y after x months.
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer.)

Answer 1

`y=-105x+1300`

Explanation:

Define the variables:

• Let x be the number of months after Zachary purchased a computer.
• Let y be the balance of the payment plan (in dollars).

Given information:

• Purchase price of the computer = $1,300
• Balance = $1,090 after 2 months.
• Balance = $565 after 7 months.

Therefore:

• x = 0, y = 1300
• x = 2, y = 1090
• x = 7, y = 565

`\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=(y_2-y_1)/(x_2-x_1)$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}`

Determine if the equation is linear by calculating the slope between each pair of (x, y) points:

`\implies \text{Slope}\;(m)=(565-1090)/(7-2)=-105`

`\implies \text{Slope}\;(m)=(1090-1300)/(2-0)=-105`

As the slope is the same, the equation is linear.

`\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}`

The initial purchase price of the computer was $1,300. So when x = 0, y = 1300. Therefore, the y-intercept is 1300.

We have already calculated the slope as -105.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:

`y=-105x+1300`