Linear equation word problem

Question

A small business buys a computer for $3600. After 4 years the value of the computer is expected to be $200. For accounting purposes the business uses linear depreciation to assess the value of the computer at a given time. This means that if V is the value of the computer at time t, then a linear equation is used to relate V and t.

 

(a) Find a linear equation that relates V (in dollars) and t (in yr).

Answer 1

So first, we need to find the rate of change over time using the numbers we were given. We know that our final amount is $200, and our initial amount is $3600. So the rate of change is equal to the difference between 3600 and 200:

 

200 = 3600 - x(4)        Subtract 3600 from both sides

-3400 = -x(4)              Multiply by -1

3400 = x(4)                Divide by 4 on both sides

850 = x                      

 

so,

 

V = 3600 - 850t

 

Now let's check our work. If we plug in 4 for t, we should get 200:

 

V = 3600 - 850(4)

V = 200

Answer 2

Use the point-slope form of the equation of a line.  We have two points for (t,V):   (0,3600) and (4,200)

 

(y-y₁) = ((y₂-y₁)/(x₂-x₁))(x-x₁)

 

 V - 3600 = (200-3600)/(4-0))(t-0)

  V - 3600 = ((-3400)/4)t

  V - 3600 = -850t

   V = -850t + 3600