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
mantaap, lengkap dan mudah d mengerti kerennnnn..
BalasHapuskeren
BalasHapusbagus,, sangat membantu,, tp kayaknya ada kesalahan di nomor 5 poin f..
BalasHapus#maaf kalo salah
kok cuma ampe no 5 aja ga ampe 9
BalasHapusMenurut saya ada yg salah
BalasHapuskk ini kelanjutan soalnya mana ?
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aq butuhh :'(
Kaka boleh lihat jelasnya, ini soalnya berantakan
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