Intercepts

Intercept: where a line crosses an axis

On normal graphs, we have the x and y intercepts.  As one might guess, the x-intercept is where a graphed line crosses the x-axis and the y-intercept is where it crosses the y-axis.

The graph below is a graph of the equation y = 4x + 8.

(There should be arrows on both ends, but as always, I am excel drawing challenged.)  If you cannot see, the line crosses the x-axis at point (-2,0) and the y-axis as (0,8).

An intercept is the point in which the other axis' coordinate is equal to 0.
So the x-intercept is the point when y = 0, and the y-intercept is the point when x = 0.

Therefore, you can find them without using a graph, just a table of values.  Find the x and y-intercepts of the equation:
5x + 2y = 6

 x y 0 3 6/5 0

The x-intercept is 6/5 and the y-intercept is 3.

Intercepts come in handy when doing other things with graphs, such as using slope.

Some equations do not have both x and y-intercepts.  These equations can be linear, quadratic, etc.  I will show a linear equation (in quadratics, an equation had no x-intercepts if solving it when y = 0 gives you imaginary solutions).

x = 4
Ok.  Find the x-intercept.  When y = 0, x = 4 (still, because x = 4 no matter what).  With that same reasoning, x can never equal 0, because it always equals 4.  Therefore, there is no y-intercept.

If you want, find the x and y-intercepts of the following equations:
1) 2x + 6 = 3y
2) x - 9 = 7y
3) y = 8