# Linear depreciation question

1. Sep 14, 2014

### !Jon Snow!

1. The problem statement, all variables and given/known data
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 $830,000, and five years after purchase, the machine is worth$500,000. Find a formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase.

2. Relevant equations
v=?

3. The attempt at a solution
This is what I got;

At T=2 V=830,000
At T=5 V=500,000

V-500,000 =[T-5][500,000-800,000]/[5-2]
C-500,000=[T-5][330,000]

Is that right?

2. Sep 14, 2014

### HallsofIvy

Staff Emeritus
Was that "C" in the last equation a typo?

You have the right formula (point- slope which I assume was given in your book) but your arithmetic is terrible! (500,000- 800,000)/(5- 2) is NOT 330,000!

3. Sep 14, 2014

### !Jon Snow!

Yes, it was a typo i meant to say "v".

Sorry, I typed this late last night.

V-500,000 =[T-5][500,000-830,000]/[5-2]
V-500,000=[T-5][-330,000]

4. Sep 14, 2014

### HallsofIvy

Staff Emeritus
Yes, so it is 830,000, not 800,000 and the fraction is negative. That is correct.
(The fact that this is depreciation tells you that the slope is negative.)