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.

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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.