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.

                     _
                |    /|
                |   /
                |  /
                | /
           (0,2)|/
                *
       (-3/2,0)/|
--------------*-+-----------------
             /  |
            /   |
           /    |
          /     |
         /      |
        /       |
      |/        |

In`ter*cept" (?), v. t. [imp. & p. p. Intercepted; p. pr. & vb. n. Intercepting.] [L. interceptus, p. p. of intercipere to intercept; inter between + capere to take, seize: cf. F. intercepter. See Capable.]

1.

To take or seize by the way, or before arrival at the destined place; to cause to stop on the passage; as, to intercept a letter; a telegram will intercept him at Paris.

God will shortly intercept your breath. Joye.

2.

To obstruct or interrupt the progress of; to stop; to hinder or oppose; as, to intercept the current of a river.

Who intercepts me in my expedition? Shak.

We must meet first, and intercept his course. Dryden.

3.

To interrupt communication with, or progress toward; to cut off, as the destination; to blockade.

While storms vindictive intercept the shore. Pope.

4. Math.

To include between; as, that part of the ine which is intercepted between the points A and B.

Syn. -- To cut off; stop; catch; seize; obstruct.

 

© Webster 1913.


In"ter*cept` (?), n. Math.

A part cut off or intercepted, as a portion of a line included between two points, or cut off two straight lines or curves.

 

© Webster 1913.

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