In a two dimensional case, the form of the linear function can be obtained if we know the co-ordinates of two points on the straight line. Suppose  x' and  x"  are two given values and the corresponding y values are  y' and y" .

Then the slope of the line is:

m

=

The intercept is

a

=

In the n dimensional case, we need the co-ordinates of at least n points for finding the linear functional form.

Example 

Find the line relating Sales (Y) to Advertizing Expenditure (X) if

X:        20         23        26       29
Y:       160       172      184     196

If we assume that the 4 points (20, 160), (23, 172), (26, 184) and (29, 196) will fall on a straight line, then we may compute 'a' and 'm' using any pair of points.

m      =       (172 - 160)/(23 - 20) = 4,

a       =       160 - (4 x 20) = 80 and

y       =       80 + 4x

One may verify that all 4 points fall on the line.

For example, consider the point (29, 196)

80 + (4 x 29) = 196