Mathematics : Plane Analytical Geometry

Straight line

Theorem 1:
Any equation of the first degree in two variables (x, y), on a two dimensional plane, represents a straight line.

Theorem 2:
Any straight line on a given coordinate plane, can be described by an equation of the first degree in two variables (x, y) ^(*).

^(*) The meaning is not ONE EQUATION ! We can have infinite equations changing k, (k ≠ 0) in kax + kby + kc = 0 (general equation of a straight line).

Symbols:
(SI)=Slope Y-Intercept equation, (GE)=General equation, (Sl)=Slope

_______ EQUATION AND SLOPE

___ Slope (given two points (P₁, P₂))

_______ SOME SPECIAL STRAIGHT LINES

___ Line passing through origin

___ Equation of the Bisector of I and III quadrant

___ Equation of the Bisector of II and IV quadrant

___ Line parallel to x-axis (1), y-axis (2)

___ Equation of x-axis (1), y-axis (2)

___ Line passing through one point: P(x₀; y₀)

___ Line passing through two points: P₀(x₀; y₀), P₁(x₁; y₁)

_______ CONDITION FOR TWO LINES TO BE PARALLEL

_______ CONDITION FOR TWO LINES TO BE PERPENDICULAR

_______ FAMILY OF STRAIGHT LINE

___ PARALLEL FAMILY (k=changes; m=costant)

_______ DISTANCE FROM A POINT (P) TO A LINE (r)

_______ ANGLE (α) BETWEEN TWO LINES

_______ BISECTORS OF THE ANGLES BETWEEN TWO LINES