Question 1039931
A machine is now worth $120,000 and will depreciate 
linearly over an 8-year period at which time it will 
be worth $25,000 as scrap. What will the machine be 
worth in 6 years?
<pre><b>
Here is a graph to explain what you're being asked.
The word "<font color="red">line</font>arly" tells us that a <font color="red">line</font> is involved.

{{{drawing(400,200,-1,12,-1,6,

circle(0,4.8,0.15),circle(0,4.8,0.13),circle(0,4.8,0.11),circle(0,4.8,0.09),circle(0,4.8,0.07),circle(0,4.8,0.05),circle(0,4.8,0.03),circle(0,4.8,0.01),

circle(8,1,0.15),circle(8,1,0.13),circle(8,1,0.11),circle(8,1,0.09),circle(8,1,0.07),circle(8,1,0.05),circle(8,1,0.03),circle(8,1,0.01),

circle(6,1.95,0.15),circle(6,1.95,0.13),circle(6,1.95,0.11),circle(6,1.95,0.09),circle(6,1.95,0.07),circle(6,1.95,0.05),circle(6,1.95,0.03),circle(6,1.95,0.01),
line(0,-2,0,7), locate(7.9,0,8),locate(5.9,0,6),locate(3.875,0,4),locate(1.85,0,2),
locate(-.1,0,0),
line(-1,0,8,0),line(0,4.8,8,1),locate(.13,5.2,"(0,$120000)"),
locate(6.13,2.5,"(6,$?????)"),locate(8.2,1.2,"(8,$25000)") )}}} 

The point (0,$120000) represents the fact that when no (zero)
years have passed, that is, when the machine is brand new,
the machine is worth $120000.

The point (8,$25000) represents the fact that when 8 years have
passed, the machine is to be scrapped, the machine is worth 
$25000 as scrap.

You are being asked to find the value $????? of the machine after
6 years have passed.

So x = the number of years
And y = how much the machine is worth in x years.

That means we need to find the equation of the line
above that goes through the points (x<sub>1</sub>,y<sub>1</sub>) = (0,120000) and
the point (x<sub>2</sub>,y<sub>2</sub>) = (8,25000)

We use the slope formula to find the slope m:

{{{m}}}{{{""=""}}}{{{(25000-120000)/(8-0)}}}{{{""=""}}}{{{(-95000)/(8)}}}{{{-11875}}}

Now we have the slope m = -11875.

We know that the equation of a line is

y = mx + b

where m = -11875 and since the y-intercept is (0,b) = (0,120000),
we can substitute m = -11875 and b = 120000 in y = mx + b
and we will have the equation of the above line.

So all you'll have to do to find what the machine is worth
after 6 years is to substitute x = 6 in the equation you'll
find for the above line.

Edwin</pre></b>