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Equations of Straight Lines PPT Maths Class 11

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     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 
 
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FAQs on Equations of Straight Lines PPT Maths Class 11

1. What are the different forms of equations of straight lines?
Ans. The different forms of equations of straight lines are the slope-intercept form, point-slope form, and two-point form. The slope-intercept form is given by y = mx + c, where m is the slope and c is the y-intercept. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. The two-point form is given by (y - y1)/(y2 - y1) = (x - x1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
2. How can I find the slope of a straight line?
Ans. The slope of a straight line is determined by the ratio of the change in y-coordinates to the change in x-coordinates between two points on the line. It can be calculated using the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
3. Can the equation of a straight line have a negative slope?
Ans. Yes, the equation of a straight line can have a negative slope. A negative slope indicates that the line is decreasing as it moves from left to right. In the slope-intercept form, a negative slope is represented by a negative value of m.
4. How can I determine if two lines are parallel or perpendicular?
Ans. Two lines are parallel if and only if their slopes are equal. If the slopes of two lines are equal, but negative reciprocals of each other, then the lines are perpendicular.
5. How can I find the equation of a line passing through a given point and parallel to another line?
Ans. To find the equation of a line passing through a given point and parallel to another line, you need to use the point-slope form of the equation. First, find the slope of the given line. Then, substitute the coordinates of the given point and the slope into the point-slope form to obtain the equation of the line.
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