Slope Intercept form of a Linear Function

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					SLOPE
INTERCEPT
FORM OF A
LINEAR
FUNCTION
WARM-UP   (TAKS
           2006)
OBJECTIVES
 TSW investigate, describe and predict the effects of
  b, the y-intercept, in the linear equation.
 TSW identify the slope and y-intercept in a linear
  equation.
Key Concept

The slope intercept form of a
linear equation is written as
        y = mx + b
         slope   y-intercept
SLOPES
   Positive      Zero




   Negative      Undefined
SLOPE
 Ratioof the vertical change (the rise) to
 the horizontal change (the run) between
 any two points on the line.

 Slope:

              rise
           m
              run
FORMULA TO FIND THE SLOPE OF A LINE


      y2  y1
   m
      x2  x1
GRAPH THE FUNCTIONS Y = 2X, Y = 3X   AND
COMPARE WITH Y = X. (M > 0)
                   y = 2x
   m>0                        The bigger
                       y=x     the slope,
                               the steeper
                        y=½x
                               the graph of
                               the line.
                               The smaller
                               the slope,
                               less steep is
          y = 3x
                               the line.
GRAPH THE FUNCTION Y = -2X, Y = -3X    AND
COMPARE WITH Y = X AND Y = -X
 y = -2x
                                   m<0
                     y=x

                                   The bigger
                                   the slope, the
                                   steeper the
                                   graph of the
                                   line.
                        y = -½ x
           y = -3x
                        y = -x
Y-INTERCEPT
   (math) to cut off or mark off between two points,
    lines, etc. (Webster’s New World Dictionary,
    2003)

   y-intercept: the y-coordinate of a point where a
    graph crosses the y-axis.
          Means that x = 0
GRAPH THE FUNCTION F(X) = X + 4 AND
COMPARE WITH F(X) = X
                                f(x) = x + 4
                                                    The graphs have
                                       f(x) = x     the same slope,
                                                    but different
                                                    y-intercepts.




Graphs of this family are vertical translations of the graph of f(x) = x.
GRAPH THE FUNCTION F(X) = X – 5 AND
COMPARE WITH F(X) = X

                                      f(x) = x
                                                   The graphs
                                                   have the
                                                   same slope,
                                       f(x) = x – 5but different
                                                   y-intercepts.




Graphs of this family are vertical translations of the graph of f(x) = x.
GRAPH THE FUNCTION F(X) = -X + 3 AND
COMPARE WITH F(X) = -X

                                                     The graphs
                                                     have the
                                                     same slope,
                                                     but different
                                                     y-intercepts.


                                         f(x) = -x + 3

                                         f(x) = -x
Graphs of this family are vertical translations of the graph of f(x) = x.
CHOOSE THE GRAPH THAT BEST MATCHES
THE
FOLLOWING EQUATIONS

   y = 2x + 2     B
                 _____

   y = 2x – 8     D
                 _____

   y = 2x + 6   _____
                   A

   y = 2x – 3     C
                 _____


                         A B C   D
IDENTIFY THE SLOPE AND Y-INTERCEPT OF
THE FOLLOWING EQUATIONS

   y = 3x + 5        y = -3x
     m=3               m = -3
     b=5               b=0


   y = -x – 6        2y = 8x – 6
     m = -1            m=4
     b = -6            b = -3


   2x – 8 = y        4y = 4x – 1
       m=2               m=1
       b = -8            b = -¼
IDENTIFY THE SLOPE AND Y-INTERCEPT OF
THE FOLLOWING EQUATIONS

   2y – 3x = 5       2x + 4y = -8




     m = 3/2           m = -½
     b = 5/2           b = -2
WRITE AN EQUATION GIVEN THE
FOLLOWING INFORMATION

 m=7                  m = -2
 b = -2               b = -7
       y = 7x – 2           y = -2x – 7



 b = -9              m=½
 m = -3              b=-¾
       y = -3x – 9          Y = ½x – ¾
 WRITE AN EQUATION IN SLOPE-INTERCEPT
 FORM OF THE LINE SHOWN
                             10
                              9                            Slope
                              8
                              7                                m=2
                              6
                              5                            y-intercept
                              4
                              3                                b = -2
                              2
                              1                            Equation
                             0
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10          y = 2x – 2
                           -1
                           -2
                           -3
                           -4
                           -5
                           -6
                           -7
                           -8
                           -9
                       -10
 WRITE AN EQUATION IN SLOPE-INTERCEPT
 FORM OF THE LINE SHOWN
                             10
                              9                            Slope
                              8
                              7                                m = -3/2
                              6
                              5                            y-intercept
                              4
                              3                                b = -1
                              2
                              1                            Equation
                             0
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10          y = -3/2x – 1
                           -1
                           -2
                           -3
                           -4
                           -5
                           -6
                           -7
                           -8
                           -9
                       -10
 WRITE AN EQUATION IN SLOPE-INTERCEPT
 FORM OF THE LINE SHOWN
                             10
                              9                            Slope
                              8
                              7                                m=½
                              6
                              5                            y-intercept
                              4
                              3                                b=3
                              2
                              1                            Equation
                             0
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10          y = ½x + 3
                           -1
                           -2
                           -3
                           -4
                           -5
                           -6
                           -7
                           -8
                           -9
                       -10
PRACTICE WORKSHEET

				
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posted:8/6/2012
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