# 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. 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 $\left( {0,4} \right)$.