Y-intercept


Y-intercept

In coordinate geometry, the "y"-intercept is the y-value of the point where the graph of a function or relation intercepts the "y"-axis of the coordinate system.

In other words, the "y"-intercept of a function is the y-value of the point at which it intersects the line "x"=0 (the "y"-axis). Thus, if the function is specified in form "y" = "f"("x"), the "y"-intercept is easy to find by calculating "f"(0). For example, in linear equations that are in the "slope-intercept" form of "y" = "mx" + "b", the value of "b" is the "y"-intercept. In general, in polynomial expressions of form "y" = "P"("x"), where "P" is a polynomial, the constant term is the "y"-intercept of the polynomial. This is because all the other terms contain "x" and thus evaluate to zero when finding "P"(0).

If the function is undefined at "x=0", for example "y=cot(x)", it has no "y"-intercept.

If the relationship is in the form "f"("x","y") = 0, or in the form of parametric equations, the corresponding equation (equations) must be solved. As a result, some 2-dimensional mathematical relationships such as circles, ellipses, and hyperbolas can have more than one "y"-intercept. A function of form "y" = "f"("x"), however, has at most "one" "y"-intercept.

The notion may be extended for 3-dimensional space and higher dimensions, as well as for other coordinate axes, possibly with other names. For example, one may speak of the "I"-intercept of the I/V-characteristic of, say, a diode. An x-intercept, or root, is the x-value of the point where a function intersects the x-axis, or the line "y"=0. Unlike "y"-intercepts, functions of the form "y" = "f"("x") can, and often do, contain multiple "x"-intercepts.


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  • Intercept — 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}.] [1913 Webster] 1. To take or seize by …   The Collaborative International Dictionary of English

  • intercept — in·ter·cept vt: to receive (a communication or signal directed elsewhere) usu. secretly shall not be unlawful...for a person acting under color of law to intercept a wire, oral, or electronic communication where such person is a party to the… …   Law dictionary

  • Intercept — can refer to: *X intercept, the point where a line crosses the x axis *Y intercept, the point where a line crosses the y axis *Interception (American football) *Telephone tapping *Tax refund interceptee also*Interception *Interceptor …   Wikipedia

  • intercept — UK US /ˌɪntəˈsept/ verb [T] ► to stop things, people, etc. as they go to a particular place: »Police intercepted a boat carrying over a million packs of cigarettes into the country illegally. »to intercept calls/communications/emails …   Financial and business terms

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  • Intercept — 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. [1913 Webster] …   The Collaborative International Dictionary of English

  • Intercept method — Intercept method. См. Метод отрезков. (Источник: «Металлы и сплавы. Справочник.» Под редакцией Ю.П. Солнцева; НПО Профессионал , НПО Мир и семья ; Санкт Петербург, 2003 г.) …   Словарь металлургических терминов

  • intercept — (v.) c.1400, from L. interceptus, pp. of intercipere take or seize between, to seize in passing, from inter between (see INTER (Cf. inter )) + cipere, comb. form of capere to take, catch (see CAPABLE (Cf. capable)). Related: Intercepted; …   Etymology dictionary

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  • intercept — ► VERB ▪ obstruct and prevent from continuing to a destination. ► NOUN 1) an act of intercepting. 2) Mathematics the point at which a line cuts the axis of a graph. DERIVATIVES interception noun interceptor noun …   English terms dictionary

  • Intercept method — The Intercept Method , or Marcq St Hilaire method , as it is also rather inaccurately known, is an astronomical navigation method of calculating an observer s position on earth. It was originally called the azimuth intercept method because the… …   Wikipedia


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