Linear functions, Mathematics

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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 

2175_linear function.png

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

= original cost of the asset

N

= estimated economic life of the asset

X

= number of years that have elapsed.

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