The general equation of a line can be reduced into various forms of the equation of a line.
The Following are the different forms of the equation of a line.
* Slope-intercept form
* Intercept form
* Normal form
Slope-intercept form If B ≠ 0, then A
x + By + C = 0 can be written as
Intercept form If C ≠ 0, then Ax + By + C = 0 can be written as
If C = 0, then Ax + By + C = 0 can be written as Ax + By = 0, which is a line
passing through the origin and, therefore, has zero intercepts on the axes.
Normal form Let x cos ω + y sin ω = p be the normal form of the line represented
by the equation Ax + By + C = 0 or Ax + By = – C. Thus, both the equations are
same and therefore,
Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is called the general linear equation or general equation of a line.
The Following are the different forms of the equation of a line.
* Slope-intercept form
* Intercept form
* Normal form
Slope-intercept form If B ≠ 0, then A
x + By + C = 0 can be written asIntercept form If C ≠ 0, then Ax + By + C = 0 can be written as
If C = 0, then Ax + By + C = 0 can be written as Ax + By = 0, which is a linepassing through the origin and, therefore, has zero intercepts on the axes.
Normal form Let x cos ω + y sin ω = p be the normal form of the line represented
by the equation Ax + By + C = 0 or Ax + By = – C. Thus, both the equations are
same and therefore,
Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is called the general linear equation or general equation of a line.
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