Question

A business woman buys a new computer for $2800. for each year that she uses it the value goes depreciates by $350 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 $1400

Answer 1

Line equation

We have a situation that can be represented with the following graph:

We have that the price decreases over time.

What does the x intercept mean in this situation?

We have that the line intercepts x-axis when y=0. This means, that it intercepts x-axis when the price is 0. The x-intercept means that the price is 0.

Find the x intercept

We know that the line reaches its x-intercept when y=0. Then we replace y by 0 in the equation:

y= -350x + 2800

↓

0= -350x + 2800

And now we solve it for x:

0= -350x + 2800

↓ taking 2800 to the left side

-2800= -350x

↓ taking -350 to the left side

-2800/-350=x

-2800/-350=8=x

Then x=8 is the x-intercept. After 8 years the price of the computer will be 0

After how many years will the value of the computer be $1400?

Its price will be $1400 when y=1400. We want to find x. We replace y by 1400 in the equation:

y= -350x + 2800

↓

1400= -350x + 2800

And now we solve it for x:

1400= -350x + 2800

↓ taking 2800 to the left side

1400-2800= -350x

-1400=-350x

↓ taking -350 to the left side

-1400/-350=x

-1400/-350=4=x

x = 4

After 4 years the price of the computer will be $1400.