SOLUTION: a business purchaseda new van for $27,500. after 5 years it's depreciated vaule is $12,000. assuming a straight line depreciation write an equation of the line giving the value V o

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Question 224579: a business purchaseda new van for $27,500. after 5 years it's depreciated vaule is $12,000. assuming a straight line depreciation write an equation of the line giving the value V of the van in terms of the age X of the van.
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(6938) About Me  (Show Source):
You can put this solution on YOUR website!
a business purchaseda new van for $27,500. after 5 years it's depreciated vaule is $12,000. assuming a straight line depreciation write an equation of the line giving the value V of the van in terms of the age X of the van. 

When X = 0 years, V = $27500
When X = 5 years, V = $12000

So we can use the usual letters for finding equations of lines,
let's use x for X and y for V:

When x = 0 years, y = $27500
When x = 5 years, y = $12000

So the problem becomes:

Find the equation of the line through the points 
(0,27500) and (5,12000)

Use the slope formula:

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m=%2812000-27500%29%2F%285-0%29=%28-15500%29%2F5=-3100

Now use the point-slope form:

y-y%5B1%5D=m%28x-x%5B1%5D%29

y-27500=-3100%28x-0%29

y-27500=-3100x

y=-3100x%2B27500

Now change x back to X and y back to V:

V=-3100X%2B27500

Edwin


Answer by MathTherapy(639) About Me  (Show Source):
You can put this solution on YOUR website!
a business purchaseda new van for $27,500. after 5 years it's depreciated vaule is $12,000. assuming a straight line depreciation write an equation of the line giving the value V of the van in terms of the age X of the van.

Age of van = X

Since in 5 years, the van depreciated to $12,000, then its annual depreciation amount is: $3,100 (%28%2427500+-+12000%29%2F5).

Since its annual depreciation is $3,100, then it's losing $3,100 of its value every year

Therefore, BOOK value of van, in any given year is: highlight_green%28V+=+27500+-+3100X%29