Minggu, 27 November 2011

KEMIRINGAN

KEMIRINGAN

1.      Carilah kemiringan (slope) garis yang telah ditentukan oleh titik A dan B berikut ini :

a.       A (3,4) B (4,3)                                          b.     A(4,5) B(8,13)
Penyelesaian
y - y1     =    x - x1                                                                 y – 5   = x - 4
y2 - y1        x2 – x1                                                           13 – 5 = 8 - 4
y – 4      =  x – 3                                                   y – 5  = x - 4
3 – 4      =  4 – 3                                                      8     =    4
y – 4      =  x – 3
   -1               1

1(y – 4) = -1 (x – 3)                                           4 (y – 5) =  8(x – 4)
y – 4      = -x + 3                                               4y – 20   = 8x - 32 
x + y      = 3 + 4                                                4y           = 8x – 32 + 20
x + y      = 7                                                       4y           = 8x - 12         
      y      = 7 – x = -x + 7                                   y             = 8/4x - 12/4
                          m = -1                                      y             =  2x - 3
                                                                          m            =  2

           c    A(-2,2),B(5,5)                                            d.     A(3,2) B(6,8)
                y – (-2)  = x – (-2)                                               y – 2        = x - 3 
                5 - 2       = 5 – (-2)                                               8 – 2        = 6 - 3
                y – 2      = x + 2                                                   y – 2        = x - 3 
                   3                7                                                        6                 3                 
               7 (y – 2) = 3 (x + 2)                                              3 (y – 2) = 6 (x – 3)                                   
               7y – 14   = 3x + 6                                                 3y – 6      = 6x - 18                                      
               7y – 3x   = 6 + 14                                                 3y            = 6x – 18 + 6                          
              -3x + 7y  = 20                                                       3y            = 6x - 12                                  
               7y   = 20 + 3x                                                            y         = 6/3 – 12/3                            
y    = -20/7 + 3x/7                                                    y          = 2x - 14
               m   =  3/7                                                                  m         = 2

e. A(A(-5,2) B(5,6)                                           f.      A(3,-5) B(8,9)
    y – 2              =   x + 5                                           y – (-5)    = x -3
    6 – 2              =   5 – (-5)                                       9 – (-5)    = 8 - 3
    y – 2              =   x + 5                                           y + 5        = x - 3
      4                        10                                                12               5
    10 (y – 2)      = 4 (x + 5)                                       5(y +5)    = 14 (x – 3)
     10y – 20       = 4x + 20                                         5y + 25    = 14x - 42
     10y               = 4x + 20 + 20                                                     5y   = 14x – 42 - 25
     10y               = 4x + 40                                                  5y   = 14x - 67
     y                   = 4/10x + 4                                               y     = 14/5x – 67/5
     m                  = 4/10                                                       m    = 14/5
     m                  = 2/6


2.      Carilah kemiringan (slope) dari garis berikut ini
a.       x = 4          :  m = tak tentu
b.      y = x + 2    :  m = 1 (positif)
c.       2x – 3y = 5
-3y        = -2x + 5
y           = -2/3 + 5/3
m          = -2/3 (negative)
            d.   y =5           : m = 0
            e.   y = 2x + 3  : m = 2 (positif)
            f.   5y + 6x  = 0
                         5y  = -4x
                           y  =  -4/5x
                           m = -4/5

3.      Tulislah persamaan – persamaan berikut ini dalam bentuk slope intercept
a.       2x – 3y – 6 = 0
      -3y = 6 – 2x = y = -6/3 + 2/3x
            b.   3x – 4y      =  9
                              -4y = 9 – 3x
                              y    = -9/4 – 3/4x
            c.   3x + 4y + 1 = 0
                             4y   = -1 – 3x
                               y   = -1/4 – 3/4x
            d.  6x – 14y     = 21
                        -14y     = 21 – 6x
                          y        = -21/4 + 6/14x
            e.  2x – 3y + 2 = 0
                        -3y       = -2 -2x
                           y       = -2/3 + 2/3x
            f.  4x – 6y        = 10
                        -6y       = 10 – 4x
                        y          = 10/6 + 4/6x














4.      Carilah kemiringan dan titik potong sumbu y pada setiap garis – garis berikut ini :
a.       3x – 2y + 12          = 0                                                       titik potong sumbu y
         -2y          = -3x – 12                                            (0,6)
         y             = 3/2x + 6                    3   (0,3)
         m            = 3/2
                                                                2         0
b.   x – y   = 0
            -y   = -x
            y    = x               titik potong sumbu y (0,0)

c    x + 5y – 10 = 0
            5y        = -x + 10
            y          = -1/5 + 2
            m         = -1/5   titik potong sumbu y (0,2)

d.      2x – 5y – 10 = 0
-5y          = -2x + 10
 y            = 2/5 – 2
m            = 2/5             titik potong sumbu y (0,-2)

            e.   3x + 2y – 15 = 0
                        2y           = -3x + 15
                         y            = -3/2 x + 15/2
                        m            = -3/2            titik potong sumbu y (0,15/2)
           
            f    -3x + 4y     = 8
                          4y      = 8 + 3x
                           y       = 2 + 3/4x
                          m       = 3/4                titik potong sumbu y (0,2)


















5.      Untuk setiap pasangan titik-titik koordinat (x,y) carilah persamaan garis lurus y=a0 + a1x
a.       (0,0) , (6,3)                                                d.  (4,-2) (0,6)
y – 0 = x – 0                                                    y – (-2)   =  x - 4
3 – 0 = 6 – 0                                                    6 – (-2)   =  0 - 4
y       = x – 0                                                    y + 2       =  x - 4
3       =   6                                                        6 + 2       =   -4
6y     = 3(x – 0)                                               -4 (y + 2)= 8(x – 4)
6y     = 3x                                                        -4y – 8    =  8x - 32
y       = 3/6x                                                     -4y          =  8x – 32 + 8
                                                                        -4y          = 8x – 24
                                                                          y           = -2x + 6

b.      (3,5) , (10,2)                                              e.   (2,2) (10,12)
y – 5      = x – 3                                               y – 2     =  x - 2
2 – 5      = 10 – 3                                             12 – 2   =  10 - 2
y – 5      =  x – 5                                              y – 2     =  x - 2
  -3         =    7                                                     10      =     8
7(y – 5)  = -3(x – 3)                                        8(y – 2) = 10 (x – 2)
7y – 35   = -3x + 9                                                      8y – 16  = 10x - 20
7y           = 3x + 9 + 35                                         8y    = 10x – 20 + 16
7y           = -3x + 44                                              8y    =  10x - 4
y             =  -3/7x + 44/7                                       y      = 10/8 – 4/8

c.       (-6 , -4) (10,8)                                            f.  (12,0) , (6,9)
y – (-4)       =  x + 6                                        y – 0         =  x - 12
8 – (-4)      =  10 – (-6)                                   9 – 10       =  6 - 12
y + 4          =  x + 6                                         y – 0         =  x - 12
8 + 4          =  10 + 6                                          9            =    -6
y + 4          =  x + 6                                        -6 (y – 0)  =  9 (x – 12)
   12           =     16                                          -6y            =  9x - 108
16 (y + 4) = 12 (x + 6)                                  -6y            =  -9/6x + 108/6
16y + 64    = 12x – 72
16y            = 12x – 72 – 64
16y            = 12x - 132


                                               

       

4 komentar:

  1. mantaap, lengkap dan mudah d mengerti kerennnnn..

    BalasHapus
  2. bagus,, sangat membantu,, tp kayaknya ada kesalahan di nomor 5 poin f..
    #maaf kalo salah

    BalasHapus
  3. kok cuma ampe no 5 aja ga ampe 9

    BalasHapus