Question

Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?

Answer 1

y = -110x + 1,600

Explanation:

Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?

1,160 - 1,050 = $110 change from month 5 to 4

Double check if the rate of decrease is steady over time:

1,600 - ($110 * 4 months) = 1,160

1,600 - ($110 * 5 months) = 1,050

This means, Zachary is paying $110 per month for his computer.

SO:

remaining payment plan balance = initial balance - 110 per month

This can be modeled by the algebraic equation:

y = 1,600 - 110x

rearrange right side:

y = -110x + 1,600

Answer 2

`y=-110x+1600`

Explanation:

Given information:

• Purchase price = $1,600
• Balance = $1,160 after 4 months.
• Balance = $1,050 after 5 months.

Define the variables:

• Let x be the number of months.
• Let y be the balance of the payment plan (in dollars).

Therefore:

• x = 0, y = 1600
• x = 4, y = 1160
• x = 5, y = 1050

`\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)=(1050-1160)/(5-4)=-110`

`\implies \text{Slope}\;(m)=(1160-1600)/(4-0)=-110`

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}}`

As the initial purchase price of the computer was $1,600, the y-intercept is 1600. We have already calculated the slope. Therefore, 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=-110x+1600`