When we talk about a line's intercepts, we most often mean the xintercept and the yintercept. These are locations where the line intercepts or crosses the x or y axis. A more formal definition is as follows:
Below is the graph of a line, with both intercepts shown:
Notice that the xintercept always has a ycoordinate of 0, and the yintercept always has an xcoordinate of 0.
Keeping the above note in mind, we can easily identify intercepts from a table of x and y values when we notice that one of the coordinates is zero! Take a look:
x  y 

2  18 
0  12 
2  6 
4  0 
6  6 
We see that the second pair (0, 12) contains a zero. In this coordinate pair, the xcoordinate is zero, which means this represents a yintercept. The yintercept of the line is at the point (0, 12). We also notice a zero in the coordinate pair (4, 0). In this case, the ycoordinate is zero, so this is the xintercept. The line crosses the xaxis at the point (4, 0).
How can we use the equation of a line to find its x– and y– intercepts? A common form of a line is in slopeintercept form: y = mx+b. This form is called slopeintercept form, because b represents the ycoordinate of the yintercept (and we know that its xcoordinate is 0). We can also use the equation in this form to find the xintercept. Since xintercepts have a ycoordinate of 0, we set the equation equal to zero and solve for x. This is shown in the example below:

Our Equation  

When we have the equation y=mx+b, the variable b is the ycoordinate of the yintercept  

For the yintercept, the xcoordinate is always 0  

To find the xintercept, plug 0 in for y as the ycoordinate is always 0  

Subtract 8 from both sides  

Divide by 2. This is the xcoordinate of the xintercept  

For the xintercept, the ycoordinate is always 0 
For the equation y = 2x + 8, the yintercept is at (0,8) and the xintercept is at (4,0).