In mathematics, specifically in graphing functions, an intercept is the point that a graph crosses any major axis (e.g., the point where a graph crosses the y-axis is called the y-intercept).
For an equation y=a*x+b, b is called the 'y-intercept'. With a little manipulation, this equation becomes x=y/a-b/a, and -b/a is then the 'x-intercept'. For this reason, the equation form y=ax+b is called the slope-intercept form. Note that the standard form is ax+by=c; the x-intercept is c/a and the y-intercept is c/b. The standard form can be related to Euclid's Algorithm, while the slope-intercept form is usually related to graphs of functions. Note that the standard form includes all lines (including 'vertical' or 'infinite slope' lines), while the slope-intercept form does not.
For the graph below, let y=3x+2 (graph is not exact). Then the y-intercept is 2 and the x-intercept is -3/2.
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(0,2)|/
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(-3/2,0)/|
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