Punktsteigungsform Beispiel Essay

Die Punktsteigungsform oder Punkt-Steigungs-Form ist in der Mathematik eine spezielle Form einer Geradengleichung. In der Punktsteigungsform wird eine Gerade in der euklidischen Ebene mit Hilfe eines Punkts der Gerade und der Steigung der Gerade dargestellt.

Darstellung[Bearbeiten | Quelltext bearbeiten]

In der Punktsteigungsform wird eine Gerade in der Ebene, die durch den Punkt verläuft und die Steigung aufweist, als die Menge derjenigen Punkte beschrieben, deren Koordinaten die Gleichung

erfüllen. Wird die Geradengleichung nach aufgelöst, erhält man die explizite Darstellung

.

Die Gerade ist dann der Graph der Funktion mit der Funktionsgleichung

.

Beispiel[Bearbeiten | Quelltext bearbeiten]

Im Bild oben ist beispielsweise der gegebene Geradenpunkt und die Steigung , und man erhält als Geradengleichung

beziehungsweise

.

Herleitung[Bearbeiten | Quelltext bearbeiten]

Geht man von der allgemeinen Form einer Geraden

aus, dann gilt insbesondere, da der Punkt auf der Geraden liegt,

.

Wird diese Gleichung nach aufgelöst und in die allgemeine Form eingesetzt, folgt daraus

.

Durch Ausklammern von erhält man dann die Punktsteigungsform

.

Umrechnung[Bearbeiten | Quelltext bearbeiten]

Wird mit Hilfe des Steigungsdreiecks durch den Punkt und einen weiteren Geradenpunkt mittels

berechnet, erhält man die Zweipunkteform einer Geradengleichung.

Literatur[Bearbeiten | Quelltext bearbeiten]

Punktsteigungsform einer Geradengleichung

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