Graphing Linear Equation, Linear Function (First Degree Polynomial)
     
      General form of the equation of a line
      The two point form of the equation of a line
General form of the equation of a line
The linear equation Ax + By + C = 0 in two unknowns, x and y, of which at least one of the coefficients, A or B, are different then zero, is called the general form for the equation of a line.
Dividing the equation by B, where B is not 0, gives
  where  
the slope-intercept form y = mx + c of a line.
By putting C = 0 into the general form obtained is    
 the equation of the line that passes through the origin.
Setting A = 0, gives the line parallel to the x-axis.
Setting B = 0 gives the line parallel to the y-axis.
The two point form of the equation of a line
Two points P1(x1, y1) and P2(x2, y2) determine a unique line on the Cartesian plane.
Therefore, their coordinates satisfy the equation y = mx + c of the line. 
The line which passes through the point P1(x1, y1)
                       is determined by the equation      y - y1 = m(x - x1).
As the point P2(x2, y2) lies on the same line,
its coordinates should satisfy the same equation    y2 - y1 = m(x2 - x1).
That way determined is the slope   where x2 - x is not 0.  
 Thus, obtained is the equation of the line passing through the two points. 
Example:  Find the equation of the line which passes through points P(-2, 3) and Q(6, -1).
   
Beginning Algebra Contents C
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