Equations of Straight Lines PPT Maths Class 11

 Page 1


     In this module we will study about 
  
?  Various form of equation of straight lines 
        (i)  Horizontal and vertical lines 
       (ii)  Point - slope form 
       (iii) Slope - intercept form 
       (iv) Two point form 
        (v)Intercept form 
        (vi)Normal form 
? Some example problems  
? Problems for practice 
 
Page 2


     In this module we will study about 
  
?  Various form of equation of straight lines 
        (i)  Horizontal and vertical lines 
       (ii)  Point - slope form 
       (iii) Slope - intercept form 
       (iv) Two point form 
        (v)Intercept form 
        (vi)Normal form 
? Some example problems  
? Problems for practice 
 
      Various forms of Straight Lines 
  
 1.Horizontal and Vertical Lines :  
  
     If a horizontal line L is at a distance a from the x-axis,      
  then the ordinate (y-coordinate) of every point lying on    
  the line is either a or –a.  
   So the equation of the line parallel to x-axis is                                                  
   y = a or y = - a.  
  The choice of sign will depend upon the position of the   
   line is above or below the y-axis. [Refer figure (a)] 
   Simillarly,  
   Equation of the vertical line at a distance b from y-axis is     
   either  x = b or x = -b[ Refer figure (b)] 
 
Page 3


     In this module we will study about 
  
?  Various form of equation of straight lines 
        (i)  Horizontal and vertical lines 
       (ii)  Point - slope form 
       (iii) Slope - intercept form 
       (iv) Two point form 
        (v)Intercept form 
        (vi)Normal form 
? Some example problems  
? Problems for practice 
 
      Various forms of Straight Lines 
  
 1.Horizontal and Vertical Lines :  
  
     If a horizontal line L is at a distance a from the x-axis,      
  then the ordinate (y-coordinate) of every point lying on    
  the line is either a or –a.  
   So the equation of the line parallel to x-axis is                                                  
   y = a or y = - a.  
  The choice of sign will depend upon the position of the   
   line is above or below the y-axis. [Refer figure (a)] 
   Simillarly,  
   Equation of the vertical line at a distance b from y-axis is     
   either  x = b or x = -b[ Refer figure (b)] 
 
Page 4


     In this module we will study about 
  
?  Various form of equation of straight lines 
        (i)  Horizontal and vertical lines 
       (ii)  Point - slope form 
       (iii) Slope - intercept form 
       (iv) Two point form 
        (v)Intercept form 
        (vi)Normal form 
? Some example problems  
? Problems for practice 
 
      Various forms of Straight Lines 
  
 1.Horizontal and Vertical Lines :  
  
     If a horizontal line L is at a distance a from the x-axis,      
  then the ordinate (y-coordinate) of every point lying on    
  the line is either a or –a.  
   So the equation of the line parallel to x-axis is                                                  
   y = a or y = - a.  
  The choice of sign will depend upon the position of the   
   line is above or below the y-axis. [Refer figure (a)] 
   Simillarly,  
   Equation of the vertical line at a distance b from y-axis is     
   either  x = b or x = -b[ Refer figure (b)] 
 
  2.Point-slope form 
 
 Suppose P
o
(x
o
,y
o
)is a fixed point  
on the line L.  Let P(x,y) any  
arbitrary point on the line. 
 
Then by definition of slope of line  
     m = 
?? -?? ?? ?? -?? ?? . 
   i.e, y – y
o
 = m(x-x
o
) 
  
   This is the equation of the line in Slope-point form. 
                                               
Page 5


     In this module we will study about 
  
?  Various form of equation of straight lines 
        (i)  Horizontal and vertical lines 
       (ii)  Point - slope form 
       (iii) Slope - intercept form 
       (iv) Two point form 
        (v)Intercept form 
        (vi)Normal form 
? Some example problems  
? Problems for practice 
 
      Various forms of Straight Lines 
  
 1.Horizontal and Vertical Lines :  
  
     If a horizontal line L is at a distance a from the x-axis,      
  then the ordinate (y-coordinate) of every point lying on    
  the line is either a or –a.  
   So the equation of the line parallel to x-axis is                                                  
   y = a or y = - a.  
  The choice of sign will depend upon the position of the   
   line is above or below the y-axis. [Refer figure (a)] 
   Simillarly,  
   Equation of the vertical line at a distance b from y-axis is     
   either  x = b or x = -b[ Refer figure (b)] 
 
  2.Point-slope form 
 
 Suppose P
o
(x
o
,y
o
)is a fixed point  
on the line L.  Let P(x,y) any  
arbitrary point on the line. 
 
Then by definition of slope of line  
     m = 
?? -?? ?? ?? -?? ?? . 
   i.e, y – y
o
 = m(x-x
o
) 
  
   This is the equation of the line in Slope-point form. 
                                               
3. Two- point form  
Let P
1
(x
1
,y
1
) and P
2
(x
2
,y
2
) be two  
points passing through the line L. 
 Let P(x,y) be any general  
point on L. 
Since the three points P1,P2 and P are collinear,  
Slope of PP
1
=Slope of P
1
P
2
 
 i.e, 
?? -?? 1
?? -?? 1
 = 
?? 2
-?? 1
?? 2
-?? 1
   (OR)                                                   
y – y
1
= 
?? ?? -?? ?? ?? ?? -?? ?? (x – x
1
)   
This is the equation of the line in two point form