Graphing Linear Equation, Linear Function (First Degree Polynomial)
     
      Slope-intercept form of a line
      Properties of the linear function
Slope-intercept 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 slope-intercept form.
The graph of the function  f (x) = mx + c intersects the y-axis at the point P0(0, c). 
Every point on the y-axis has abscissa 0 that is, x = 0 denotes the y-axis.  
Thus, we find the y-intercept by calculating   f (0) = m 0 + c,      f (0) = c
Every point on the x-axis has ordinate 0 that is,  y = 0 denotes the x-axis.  
Therefore, the intersection point of the graph and the x-axis 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 x-intercept
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 x-axis 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 (x1) <  f (x2)   for all  x1 < x2
If m < 0 linear function decreasing,   f (x1) >  f (x2)   for all  x1 < x2    i.e., the graph falls from left to right.
Beginning Algebra Contents C
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