4.Diketahui beberapa garis dengan persamaan berikut : Garis k: 2x+3y-5 =0 Garis : y = ²x +7 Garis m y=-x +6 Garis n 3x-2y +9 =0

JAWABAN :

1) 4x – 2y + 5 = 0 – 1/2y = – 4x – 5 gradien saling tegak lurus

m = – 4-1/2

m = 8

m1. m2 = – 1 8. m2 = 1

m2 = 1/8

2) (y – y1)/(y2 – y1) = (x-x1)/(x2-x1)

(y-2)/(-1-2) = (x + 3) / ( 5 + 3) (y-2)/-3 = (x + 3) / 8

8 (y-2)=-3 (x + 3)

8y- 16 = 3x – 9 8y + 3x = -9 + 16

8y + 3x = 7

3) y = 3/2 x + 9 m = 3/2

gradien saling tegak lurus

m1. m2 = 1 3/2 m2 = – 1

m2 = 2/3

pera garis

y – y1= m ( x – x1)

y + 3 = -2/3 (x + 2)

y=-2/3 x – 4/3 – 3 ( dikalikan 3)

(4. ) (y – y1)/(y2 – y1) = (x-x1)/(x2-x1) (y-O)/(3-0) = (x – 0) / (2-0)

y/3 =x/2

2y = 3x

2y – 3x = 0

3y = 7 – 6x

m = -6/3

m = -2

gradien saling tegak lurus

m1. m2 = -1

– 2. m2 = -1

m2 = 12

pers garis

y – y1= m ( x-x1)

y + 2 = 1/2 (x-4) y = 12x-2-2

y = 1/2 x – 4 (dikali 2)

2y = x – 8

2y-x+8 = 0

persamaan yg gradienya 3:

c) 6x – 2y = 12

– 2y = – 6x + 12

m = -6/-2

m = 3

5) 3x – 6y + 5 = 0

– 6y=-3x – 5

m = -3/-6

3y – 2x – 49 3y + 2x = – 13

6) 4x – 2y = 6

– 2y = – 4x + 6

m = -4/-2

m = 2

7) 3x – 2y = 6 – 2y = – 3x + 6 m = 3/2

m = -3/-2

gradien saling sejajar m1 = m2 = 3/2

pers garis

y – y1= m ( x-x1) y = 3/2 x – 9-6 y = 3/2 x 15 ( dikali 2)

y + 6 = 3/2 (x – 6)

2y = 3x – 30

2y – 3x + 30 = 0

8) 3x – 5y = 10

– 5y = – 3x + 10

m = -3/-5

m = 3/5

9) y – y1= m ( x – x1) y-x+8 = 0

y + 5 = 1(x-3) y=x-3-5

y = x – 8

10) x – 2y + 4 = 0

– 2y = -x – 4

11) 3x + 7y – 9 = 0

7y=-3x + 9

m = -3/7 gradien saling tegak lurus

m1. m2 = 1

– 3/7. m2 = -1

m2 = 7/3

pers garis y – y1= m ( x – x1)

y + 1 = 7/3 (x-6)

y = 7/3x – 14 – 1

y = 7/3 x 15 (dikali 3)

3y = 7x – 45 3y – 7x + 45 = 0

12) m = (y2 – y1)/(x2-x1) m = (-8+3)/(3-5)

m = -5/-2

m = 5/2

13) y = 2/3x + 9

pers garis

y – y1= m ( x – x1)

m = 23 3y = 2x + 2-9

y + 3 = 2 ( x + 1) y = 23 x + 2/3-3 (dikali 3)

3y – 2x = -7

(14) y = – 3x + 2

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