Question

Zac purchased a new car for $23995 . The value of the car linearly depreciated to $9300 over 10 years . Write a linear equation to represent the value of Y of zacs car ( in dollars ) after X years since it’s purchase

Answer 1

Given that:

- The initial value of the car was $23995.

- Its value linearly depreciated to $9300 over 10 years.

- The variable "y" represents the value of Zac's car (in dollars) and "x" represents the number of years since it’s purchased.

You need to remember the Slope-Intercept Form of the equation of a line:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

In this case, the value of "b" is the initial value of the car when it was purchased by Zac:

$b=23995$

By analyzing the data given in the exercise, you can identify this point:

$(10,9300)$

Where:

$\begin{gathered} x=10 \\ y=9300 \end{gathered}$

Therefore, you can substitute all the known values into the following equation and solve for the slope "m":

$y=mx+b$

Then, you get:

$\begin{gathered} 9300=m(10)+23995 \\ \\ 9300-23995=10m \end{gathered}$

$\begin{gathered} -14695=10m \\ \\ \frac{-14695}{10}=m \\ \\ m=-1469.5 \end{gathered}$

Knowing "m" and "b", you can set up the following equation to represent this situation:

$y=-1469.5x+23995$

Hence, the answer is:

$y=-1469.5x+23995$