
Graphing
Linear Equation, Linear Function (First Degree Polynomial)



Slopeintercept form of a line

Properties
of the linear function






Slopeintercept form of a line

By moving the graph of the linear function
f (x)
= mx
vertically by
the vector c, 
obtained is the linear function 
f
(x)
= mx
+ c, 


every
point of which has the y value that differs from the source graph
f (x)
= mx by
the same constant c. 
This form of the linear function is called the
slopeintercept form. 



The graph of the function
f (x)
= mx
+ c
intersects the yaxis at the
point P_{0}(0,
c). 
Every point on the
yaxis has abscissa
0 that is, 
x
= 0 
denotes the
yaxis. 


Thus, we find the
yintercept by calculating
f
(0)
= m
· 0
+ c,
f
(0)
= c. 
Every point on the
xaxis has ordinate
0 that is, 
y
= 0 
denotes
the
xaxis. 


Therefore, the intersection point of the
graph and the xaxis we calculate from the equation
f (x)
= 0. 
Thus
solving for x, 
0
= mx
+ c, 
we get 

the root or
the zero point or the xintercept 

of the
linear function f
(x)
= mx
+ c. 

Example:
Find the equation of the line that passes through the points A
(4,
1)
and B (6,
4). 



Properties
of the linear function

We examine the behavior of a function
y =
f
(x)
by moving from left to right in the direction of xaxis by inspecting its graph. 
The linear
function f (x)
= mx
+ c,
m
> 0 is increasing, the graph rises from left to right, that is, 
f
(x_{1})
< f
(x_{2})
for all
x_{1
}< x_{2} 


If
m
< 0 linear function decreasing,
f
(x_{1})
> f (x_{2}) for all
x_{1
}< x_{2 }i.e., the graph falls from left to right. 










Beginning
Algebra Contents C 



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