The general equation or standard equation of a straight line is given by
Let be a point which does not lie on the line (i). Now draw a perpendicular line from to the X-axis through the point as shown in the given diagram. It is clear from the diagram that is the abscissa of the point . If is the ordinate of , then are the coordinates of . Since lies on the line (i), it must satisfy the equation of the line, i.e.
Next we consider the difference , i.e.
(a) If the point is above the line, then . From equation (iii), we note that only if . But if and or if and .
We conclude that the point is above the line if
(b) If the point is below the line, then . From equation (iii), we note that only if . But if and or if and .
We conclude that the point is below the line if
NOTE: The point will be on the line if .
Example: Determine whether the point lies below or above the line .
Comparing the given line with the general equation of line , we have , and .
Since is the given point, then .
Since and , the given point lies above the line.