a company purchased a computer workstation for $8000

Question

after 3 years the estimated value of the workstation was $4400. if the value v in dollars and te age a of the workstation are related by a linear equation, find an equation that express v in terms of a

Answer 1

Since this is a linear equation, we are looking for an equation that can be expressed in the form y=mx + b.  Instead of y and x, we are going to use v and a.  The equation will be v = ma + b, we have to find the values of m and b.

We will use the coordinate system (a,v) instead of (x,y).

We have two points:  (0,8000) which means the system was worth $8000 after 0 years and (3, 4400) which means the system was worth $4400 after 3 years

Slope formula states: m = (y₂ - y₁)/(x₂ - x₁), since we are using (a,v) instead of (x,y) our formula is

m = (v₂ - v₁)/(a₂ - a₁)

After substituting in our values, we have

m = (4400 - 8000)/(3 - 0)

m = - 3600/3

m = -1200

Now that we have our slope, we can substitute it into the point-slope formula to find our equation.  Point slope formual says y - y₁ = m(x - x₁).  Our variation states v - v₁ = m(a - a₁).

After substituting a point (I chose (0,8000)), we get v - 8000 = -1200(a -0)

Simplifying, we get v - 8000 = -1200a

Add 8000 to each side to get the solution:

v = -1200a + 8000