Linear functions are of the form:
y = a0 + a1 x1 + a2 x2 + ..... + an xn
where a0, a1, a2 ..... an are constants and x1, x2 ..... xn 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 Y-intercept is a and the slope of the line is m.
If m = 0; y = a is a line parallel to the X-axis.
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. |