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Intercepts

The x-coordinate of the point of intersection of a line with the x-axis represents the x-intercept. Similarly, the y-coordinate of the point of intersection with y-axis gives the y-intercept.

Equations of a line

  • The slope-intercept form of equation of a given by line is Description: 37180.png
    Description: 45310.png 
     
    Here m is called the slope of the line and c is the of y-intercept. 
  • The equation of the line passing through the point (x1, y1) can be written as ( y – y1Description: 37167.png
     
    This form is called point-slope form.
Description: 45327.png
  • Let the line pass through two points (x1 , y1) and (x2, y2).
     
    Then the equation of the line can be written as
    Description: 51700.png
     
    This form is called two point form.
    Description: 45347.png 
  • Let the line make x-intercept = a and y-intercept = b.
     
    Then, the equation of the line can be written as
     
    Description: 37139.png
     
    This form is called intercept form.
  • General equation of a line: Any linear equation in two variables represents a straight line. Thus, ax + by + c = 0 is the general equation of a line.
  • The equation of a line passing through the point of intersection of the lines
     
    ax + by + c = 0 and a1x + b1y + c1 = 0 can be written as
     
    ax + by + c + k (a1x + b1 y + c1) = 0, where k is any constant.
  • The equation of a line parallel to a line ax + by + c = 0 is given by ax + by + k = 0, where k is a constant. 
  • The equation of a line perpendicular to a line ax + by + c = 0 is given by bx – ay + k = 0, where k is a constant.

The perpendicular distance of a point (x1, y1) from a line ax + by + c = 0 is given by

Description: 37133.png 





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