Theory:

The intercept of a line is the distance from the origin to point which meets either \(x\)-axis or \(y\)-axis.
The \(y\)-intercept of the line is the point where the line meets the \(y\)-axis. Similarly, the \(x\)-intercept of the line is the point where the line meets the \(x\)-axis.
 
The intercept of a line can be expressed as \(y=mx+c\) where \(m\) is the slope of the line and \(c\) is the point where the line meets the \(y\)-axis.
Example:
Find the \(x\)-intercept and \(y\)-intercept of the given graph.
 
2 (1).png
 
Solution:
 
We know that \(y\)-intercept of the line is the point where the line meets the \(y\)-axis.
 
Hence, from the above graph, we can see that the line meets the \(y\)-axis at the point \((0,2)\).
 
Therefore, the \(y\)-intercept is \(2\).
 
Similarly, we can find the \(x\)-intercept. Since \(x\)-intercept of the line is the point where the line meets the \(x\)-axis.
 
Hence, from the above graph, we can see that the line meets the \(x\)-axis at the point \((1,0)\).
 
Therefore, the \(x\)-intercept is \(1\).