Formeln: Mathematik - Geometrie - Gerade ⁄

Gerade ⁄

Definitionen:

  • x1: x1-Koordinate
  • x2: x2-Koordinate
  • y1: y1-Koordinate
  • y2: y2-Koordinate
  • m: Steigung
  • b: y-Achsenabschnitt
  • f:
  • y: Gleichung
Layer 1 x x y y 1 1 2 2

Steigung

\( m = \frac{y_2 - y_1}{x_2 - x_1} \)
m = Steigung
y2 = y2-Koordinate
y1 = y1-Koordinate
x2 = x2-Koordinate
x1 = x1-Koordinate


Layer 1 x x y y 1 1 2 2 b

Hauptform

\( y = m \times x + b \)
y = Gleichung
m = Steigung
b = y-Achsenabschnitt

\( y = \frac{y_2 - y_1}{x_2 - x_1} \times x + \left( y_2 - \frac{y_2 - y_1}{x_2 - x_1} \times x_2 \right) \)
y = Gleichung
y1 = y1-Koordinate
y2 = y2-Koordinate
x1 = x1-Koordinate
x2 = x2-Koordinate
y2 = y2-Koordinate
y1 = y1-Koordinate
y2 = y2-Koordinate
x1 = x1-Koordinate
x2 = x2-Koordinate
x2 = x2-Koordinate

\( y = m \times x + \left( y_2 - m \times x_2 \right) \)
y = Gleichung
m = Steigung
y2 = y2-Koordinate
m = Steigung
x2 = x2-Koordinate

\( y = m \times x + \left( y_1 - m \times x_1 \right) \)
y = Gleichung
m = Steigung
y1 = y1-Koordinate
m = Steigung
x1 = x1-Koordinate


Zwei Punkte Form

\( y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} \times \left( x - x_1 \right) \)
f =
y1 = y1-Koordinate
y1 = y1-Koordinate
y2 = y2-Koordinate
x1 = x1-Koordinate
x2 = x2-Koordinate
x1 = x1-Koordinate