
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 slopeintercept 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 xaxis. 

Setting B = 0 gives 

the
line parallel to the yaxis. 


The
two point form of the equation of a line

Two points
P_{1}(x_{1},
y_{1})
and P_{2}(x_{2},
y_{2})
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
P_{1}(x_{1},
y_{1}) 
is determined by the equation y 
y_{1}
= m(x
 x_{1}). 
As the
point P_{2}(x_{2},
y_{2})
lies on the same line, 
its coordinates should satisfy
the same equation
y_{2} 
y_{1}
= m(x_{2}
 x_{1}). 
That way determined is
the slope 

where
x_{2
}
 x_{1 }
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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