☼ Equation of  a line :–

 ⟶ Parametric Equation of  a line :

{ (x, y) / x = tx₂+ (1 – t)x₁, y  = ty₂+ (1 – t)y₁ ; t ∈ R }

   ⟶ If  a line passing through two distinct points A(x₁, y₁) and B (x₂, y₂), then

Cartesian equation of  a line :   or

   ⟶ Equation of  X – axis : y = 0

   ⟶ Equation of  Y – axis : x = 0

   ⟶ The line perpendicular to X – axis ( or parallel to Y – axis )  :  x = a

   ⟶ The line perpendicular to Y – axis ( or parallel to X – axis )  :  y = b

   ⟶ The standard equation of  a line is ax + by + c = 0.

 ⟶ The perpendicular line to ax + by + c = 0 is : bx – ay + k = 0  : k ∈ R

   ⟶ The parallel line to ax + by + c = 0 is : ax + by + k = 0 : k ∈ R – { c }

   ⟶ If  a line passing through the point A (x₁, y₁) with the slope = m, then

Equation of  a line ( Slope – Point equation ) : y – y₁  = m ( x – x₁ )

   ⟶ Eq. of  a line with X – intercept = a  &  Y – intercept = b is : \frac{x}{a} + \frac{y}{b} = 1

   ⟶ Equation of  a line with slope = m and y – intercept = c  is : y = mx + c

   ⟶ If  a line passing through the point A (x₁, y₁) which makes an angle θ with positive direction of  X – axis, then equation of  a line :

=  :  Where,

   ⟶ If  length of  a perpendicular line – segment drawn from the origin to the line is  =  p and this perpendicular line – segment makes an angle α with positive direction of  X – axis, then equation of  line is ( p – α Equation ) :

x cosα  +  y sinα  =  1

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