Question

15. Tim buys a new computer for his office for $1200. For tax purposes, he declares a linear depreciation (loss of value) of $200 per year. Let y be the declared value of the computer after x years. What is the slope of the line that models this depreciation?
Find the y-intercept of the line.

Write a linear equation in slope-intercept form to model the value of the computer over time.


Find the value of the computer after 4.5 years.

Answer 1

Answer:

Slope is -200 and y-intercept is at (0, 1200)

The linear equation is:  $y=-200x+1200$

The value of the computer after 4.5 years will be $300.

Step-by-step explanation:

Value of the new computer is $1200

For tax purposes, the linear depreciation (loss of value) is $200 per year.

So after $x$ years, total loss of value will be:  $\ 200x$

If $y$ is the declared value of the computer after $x$ years, then the linear equation will be.......

$y=1200-200x\\ \\ \Rightarrow y=-200x+1200$

If we compare the above equation with slope-intercept form$(y=mx+b)$, then we will get:  $m=-200$ and $b=1200$

So, the slope of the line will be -200 and y-intercept will be at (0, 1200)

After 4.5 years means $x=4.5$

So when $x=4.5$,  $y=-200(4.5)+1200=-900+1200=300$

Thus, the value of the computer after 4.5 years will be $300.