Question

A business woman buys a new computer for $4000. for each year that she uses it the value goes depreciates by $400 the equation below gives the value y of the computer after x years. What does the x intercept mean in this situation? Find the x intercept. After how many years will the value of the computer be $2000Y=-400x+4000

Answer 1

Step 1: Write the equation

y = -400x + 4000

Step 2:

The intercept in the equation represents time in years.

x-intercept represents the total length of time taken in years for the computer to values to depreciate to $0.

step 3: Find the x-intercept

To find the x-intercept, you will have to find the time taken for the computer value to depreciate to $0.

y = $0

`\begin{gathered} \text{From the equation.} \\ y\text{ = -400x + 4000} \\ 0\text{ = -400x + 4000} \\ 400x\text{ = 4000} \\ x\text{ = }(4000)/(400) \\ x\text{ = 10} \end{gathered}`

The x-intercept = 10 years

Step 4:

To find the number of years take for the computer value to depreciate to $2000.

You will substitute the value of y = $2000 and find the value of x.

Therefore

`\begin{gathered} y\text{ = -400x + 4000} \\ 2000\text{ = -400x + 4000} \\ 400x\text{ = 4000 - 2000} \\ 400x\text{ = 2000} \\ x\text{ = }(2000)/(400) \\ \text{x = 5 years} \end{gathered}`

It will take 5 years for the value of the computer to depreciate to $2000.