Equation of Straight Line in Point-slope form, Slope-intercept form, Two-point form, Intercept form and Normal form

1. Physics Helpline
L K Satapathy
2D Geometry 2

2. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
0 0
0
y c
m y c y c
x

       

Line parallel to x-axis at a distance c from it
y = c
O x
y
c
(0, c) A P (x , y)
x=c
c
A (c,0)
P (x , y)
Y - coordinate of every point on the line = c
 Coordinates of A = (0 , c) and let P = (x , y)
1 0 0
0
x c x c x c
m y
       

Line perpendicular to x-axis at a distance c from it
X - coordinate of every point on the line = c
 Coordinates of A = (c , 0) and let P = (x , y)
1 0
m
Slope of AP is not defined ,  we put
Slope of AP is zero ,  we put m = 0
Physics Helpline
L K Satapathy

3. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
1 1( , )x y
Point Slope Form
O x
y
A
P
( , )x y
1 1( , )x y
Given point A = Given slope = m
( , )x yAny point on the line P =
1
1 1
1
( )
y y
m y y m x x
x x

    

Slope of AP =
O x
y
B
P
( , )x y(0, )b
b
Slope Intercept Form
(0, )by-intercept = b  B =
( , )x yAny point on the line P =
Given slope = m
0
y b
m y b mx y mx b
x

      

Slope of BP =
Physics Helpline
L K Satapathy

4. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
1 2 1
1 2 1
AB AC
y y y y
m m
x x x x
 
   
 
O x
y
A
P
B ( , )x y
1 1( , )x y
2 2( , )x y
Two Point Form
Given points A = and B =1 1( , )x y 2 2( , )x y
( , )x yAny point on the line , P =
2 1 1
2 1 1
,AB AC
y y y y
m m
x x x x
 
  
 
2 1
1 1
2 1
( )
y y
y y x x
x x

   

Physics Helpline
L K Satapathy

5. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
1
yx
a b
  
Intercept Form
O A
B
a
b
P ( , )x y
(0, )b
( ,0)a
Given Intercepts : ,OA a OB b 
( ,0) , (0, )A a B b  
Slope of AB
0
0AB
b bm
a a
  

Slope of AP
0
AP
y y
m
x a x a

 
 
( , )x yAny point on the line P =
1AP AB
y yb a x xm m
x a a b a a
       

Physics Helpline
L K Satapathy

6. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
cos sinx y p   
Normal Form
O A
B
a
b
C
p

Given :
,OA a OB b 
( ) ,COA OBC OC p    
Intercepts
In  COA cos
cos
p pOC a
OA a


   
In  OBC sin
sin
p pOC b
OB b


   
1 1
cos sin
y yx x
a b p p 
     
sincos 1
yx
p p
  
Physics Helpline
L K Satapathy

7. Physics Helpline
L K Satapathy
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