Question

For tax and accounting purposes, corporations depreciate the value of equipment each year. One method used is called "linear depreciation," where the value decreases over time in a linear manner. Suppose that two years after purchase, an industrial milling machine is worth $820,000, and five years after purchase, the machine is worth $430,000. Find a formula for the machine value V.

Answer 1

Answer:

$V=-130000x+1080000$

Explanation:

Linear Dependence

Some variables are known or assumed to have linear dependence which means the graph of the ordered pairs (x,V) is a straight line.

If we know two points of the line, we can come up with the exact equation and therefore make predictions for other values of x

The linear depreciation gives us these points (2,820000) and (5,430000)

The general equation of the line is

$V=mx+b$

Where V is the machine value and x is the  number of years after purchase. We need to find the values of m and b.

Replacing the first point

$820000=m(2)+b$

$2m+b=820000$

Replacing the second point

$5m+b=430000$

Subtracting them  

$-3m=390000$

$m=-130000$

Replacing in any of the equations, say, the first one

$2(-130000)+b=820000$

Solving for b

$b=820000+260000$

$b=1080000$

The formula for the machine value V is  

$\boxed{V=-130000x+1080000}$