X and Y Intercepts of a Line

When a straight line is represented graphically the following two main attributes will come out: the X-intercept and the Y-intercept of the straight line. These two concepts are very simple and easy to understand when we draw a straight line graphically.


xy-intercepts

The X-intercept occurs when we draw a straight in a Cartesian plane, i.e. XY-plane, and the straight line cuts the X-axis at one point, say a. This point of intersection is called the X-intercept of a straight line and at the point value of the Y-axis is zero, i.e. y = 0. The X-intercept is usually represented by an ordered pair: \left( {a,0} \right).

Similarly, the Y-intercept occurs when the straight line cuts the Y-axis at one point, say b. This point of intersection is called the Y-intercept of a straight line and at this point value of the X-axis is zero, i.e. x = 0. The Y-intercept is usually represented by an ordered pair: \left( {0,b} \right).

Algebraically we can find the X-intercept and Y-intercept of a straight line ax + by + c = 0 by setting the values y = 0 and x = 0 respectively.

Example: Find the X- and Y-intercepts of the given straight line: 2x + 4y = 16

To find the X-intercept put y = 0 in the above equation of a straight line:

2x + 4\left( 0 \right) = 16 \Rightarrow x = 8

Therefore, the X-intercept is \left( {8,0} \right).

Similarly, to find the Y-intercept put x = 0 in the above equation of a straight line:

2\left( 0 \right) + 4y = 16 \Rightarrow y = 4

Therefore, the Y-intercept is \left( {0,4} \right).