Intercepts are where the line crosses the x-axis and the y-axis. Where the line crosses the y-axis is called the y-axis intercept. At the point where the line crosses the y-axis, the value of x has to be 0. This gives us a clue to finding what the y-axis intercept is – all we need to do is set the value of x to zero in the relation.
So our relation from before is 
. What we need to do is
set the value of x to zero, and then see what y is equal to. This value of y
is the y-axis intercept, the point where the line crosses the y-axis:
Now on to finding the x-axis intercept. This is where the line crosses the x-axis. Now, all along the x-axis the value of y is zero. So what we need to do is set y to zero in the relation, and then work out what x is. The value of x we calculate will be the location along the x-axis where the line intercepts it:
So we’ve found that this line has a positive
gradient, an x-axis intercept at 
and a y-axis intercept at 2.
Although we didn’t have to draw a graph to find out this information, here’s
one anyway, with the intercepts shown on it.
So this is how you work out the intercepts of a straight line graph. One thing you need to remember is that vertical or horizontal lines will only have one intercept. For instance, the following relation:
is a horizontal line, which means that it only intersects the y-axis. Where does it intersect? Well that’s pretty easy, we don’t even have to do any maths, we just need to look at the relation – it intersects the y-axis at y = 3! Easy.