The x-intercept is the point at which a line crosses the
*x*
-axis; i.e. the point at which
*y* = 0
. The y-intercept is the point at which a line crosses the
*y*
-axis; that is, the point at which
*x* = 0
. These concepts depend upon writing a linear equation using variables
*x*
and
*y*
, which is both standard and implicit in our identification of such an equation with the straight line that is its graph.

To find the
*x*
-intercept, set
*y* = 0
and solve the equation. For example, to find the
*x*
-intercept of
5*y* - 2*x* = 10
:

5(0) - 2*x* = 10

-2*x* = 10

*x* = - 5

Thus, the
*x*
-intercept, or the point at which the line crosses the horizontal axis, is
(- 5, 0)
.

To find the
*y*
-intercept, set
*x* = 0
and solve the equation. For example to find the
*y*
-intercept of
5*y* - 2*x* = 10
:

5*y* - 2(0) = 10

5*y* = 10

*y* = 2

Thus, the
*y*
-intercept, or the point at which the line crosses the vertical axis, is
(0, 2)
.

Hence, **to find the intercept of either variable, set the other variable equal to 0 and solve for the original variable**.

As observed in the last section, we only really need two points to graph a line. Usually, the two easiest points to find are the
*x*
-intercept and the
*y*
-intercept. Once these have been found, we can plot them, draw a straight line connecting them, and extend the line at either end. Here is a graph of the equation
5*y* - 2*x* = 10
, drawn using intercepts:

It is important to point out that, no matter what technique we use to graph an equation, the graph of the equation is always the same -- all techniques will yield the exact same graph.