Line Intercept; what does it mean? GRE Math fact

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.

A line parallel to the X axis will have a Y intercept, but no X intercept.  If its Y intercept 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 

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

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:

 

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 

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. 

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.

The equation of the line is, 

E is the correct answer.