Is this true or false?

Question

Suppose an asset is being depreciated linearly. Then the rate of depreciation of the asset is given by the negative of the slope of the depreciation line.  If you think the statement is true, then prove it. On the other hand, if you think the statement is false, then give an example that disproves the statement

Answer 1

The statement is false. Here's an example that shows why:

 

The slope of a depreciation line is negative or downward sloping. So let's say the asset is worth $500 dollars and depreciates at a rate of $100 dollars each year. So on a coordinate plane, I start at (0,500). At the end of the 1st year, I am at (1,400). The next year brings me to (2,300) and so forth until I have fully depreciated the asset at (5,0). The slope is equal to the rise over the run. So pick two points I just listed, let's say (0,500) and (1,400). The rise is -100 (it falls 100 dollars) while the run is 1. So the slope is equal to -100/1 or -100. The problem states that the depreciation is equal to the NEGATIVE of the slope of the depreciation line. Well, we just found that the slope of the depreciation line is equal to -100 and the NEGATIVE of -100 is equal to -(-100) which is equal to a POSITIVE 100. So the problem is saying the rate of depreciation is equal to positive 100. However, we know that the depreciation of an asset is always negative and therefore this statement must be false. 

 

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