Linear functions are of the form:

y = a₀ + a₁ x₁ + a₂ x₂ + ..... + a_n x_n

where a₀, a₁, a₂ ..... a_n are constants and x₁, x₂ ..... 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 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: