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.

<pre><font size = 4 color = "indigo"><b>
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=(y[2]-y[1])/(x[2]-x[1])}}}

{{{m=(12000-27500)/(5-0)=(-15500)/5=-3100}}}

Now use the point-slope form:

{{{y-y[1]=m(x-x[1])}}}

{{{y-27500=-3100(x-0)}}}

{{{y-27500=-3100x}}}

{{{y=-3100x+27500}}}

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

{{{V=-3100X+27500}}}

Edwin</pre>