Linear functions are of the form:
y = a_{0} + a_{1} x_{1} + a_{2} x_{2} + ..... + a_{n} x_{n}
where a_{0}, a_{1}, a_{2} ..... a_{n} are constants and x_{1}, x_{2} ..... x_{n} are n variables. (These functions are used in regression).
In a two dimensional space, a linear function is a straight line and is usually written as y = a + mx.
The Yintercept is a and the slope of the line is m.
If m = 0; y = a is a line parallel to the Xaxis.
If m > 0; as x increases, y increases. The line rises from left to right.
If m < 0: As x increases, y decreases. The line falls from left to right.
This is illustrated below.
Figure
Example
Straight line depreciation is a linear function of the number of years that have elapsed. This can be expressed in a functional form as:
BV

= 
C  
[C/N] 
X 
where, 




BV

= 
book value of the asset 
C

= 
original cost of the asset 
N

= 
estimated economic life of the asset 
X

= 
number of years that have elapsed. 