Any line that is not parallel to an axis will intersect both the X and the Y axes. The non-zero coordinates of the points at which the line intersects the axes, are said to be the intercepts of the line. For example, in the following figure the X and Y-intercept of the line is 3:
The most common format to represent the equation of a line is 
where 
is the value of the 
intercept i.e. the coordinate of the point where the line crosses the -axis, and 
is the slope of the line.
where is the value of the intercept i.e. the coordinate of the point where the line crosses the -axis, and is the slope of the line.
A line parallel to the X axis will have a Y intercept, but no X intercept. If its Y intercept is 
, its equation is 
, its equation is
A line parallel to the Y axis will have only an X intercept, but no Y intercept. If its X intercept is 
, its equation is 
, its equation is
A line passing through the origin will have a 0 intercept for the Y axes, and can be written as 
where is the slope of the line
where is the slope of the line
The equation of a line can also be written in terms of X and Y intercepts. For example, a line intersects X axis at point 
and Y axis at point 
will have X and Y intercepts as and respectively. It is possible to represent the line using the intercepts. The equation for this line will be:
and Y axis at point will have X and Y intercepts as and respectively. It is possible to represent the line using the intercepts. The equation for this line will be:
This formula is known as the equation of the line in intercept form:
If a line has an equal intercept, , on both the X and the Y axes, its equation is 
, on both the X and the Y axes, its equation is
If a line has an X and Y intercept that are equal in magnitude, but opposite in sign (i.e. one is positive and the other is negative), its equation is 
(where is the intercept on the X axis, and - is the intercept on the Y axis.
(where is the intercept on the X axis, and - is the intercept on the Y axis.
Let us look at an example:
Example:
What is the equation of a line that has equal intercepts on the axes and passes through point (2, 2)?
A) 
B) 
C) 
D) 
E) 
Solution:
The equation of a line having equal intercepts on both axes is,
We know that this this line passes through point (2,2) , therefore ; 
should satisfy this equation.
should satisfy this equation.
The equation of the line is,
E is the correct answer.
