1. bentuklah persamaan linear yang garisnya melalui pasangan titik-titik berikut

a. (4 : –2) & (0 : 6)

b. (2 : 2) & (10 : 12)

Jawab

a. A (4 : –2) & B (0 :6)

Dik : X₁ = 4

X₂ = 0

Y₁ = –2

Y₂ = 6

Penyelesaian:

X – X₁ Y – Y₁

————— = —————

X₂ – X₁ Y₂ – Y₁

X – 4 Y – (–2)

————— = —————

0 – 4 6 – (–2)

X – 4 Y + 2

————— = —————

0 – 4 6 + 2

X + 4 Y + 2

————— = —————

–4 8

8 (X –4) = –4 (Y + 2)

8X – 32 = –4Y –8

8X = –4Y + 32 + 8

8X = –4Y + 24

X = –4Y + 24

—————

8

X = –4Y 24

—— + ——

8 8

X = –4

—— + 3

8Y

b. (2 : 2) & (10 : 12)

Dik : X₁ = 4

X₂ = 0

Y₁ = –2

Y₂ = 6

Penyelesaian:

X – X₁ Y – Y₁

————— = —————

X₂ – X₁ Y₂ – Y₁

X – 2 Y – 2

————— = —————

20 – 2 12 – 2

X + 2 Y – 2

————— = —————

8 10

10 (X – 2) = 8 (Y – 2)

10X – 20 = 8Y – 16

10X = 8Y + 4

X = 8Y + 4

—————

10

X = 8Y 4

—— + ——

10 10

2. untuk setiap tittik koordinat (X : Y) & koofisien kemiringan berikut ini. Carilah persamaan garis lurus!

a. (–1 : 3) & b= 5

b. (–1 : 3) & b= 2

Jawab

a. (–1 : 3) & b= 5

Y – Y₁ = b (X – X₁)

Dik: X₁ = –1

Y₁ = 3

b = 5

penyelesaian:

Y –Y₁ = b (X –X₁)

Y – 3 = 5 (X – (–1)

Y – 3 = 5 (X + 1)

Y – 3 = 5 X + 5

Y = 5 X + 5 + 3

Y = 5X + 8

b.

3. carilah kemiringan / lereng / koofisien arah berikut ini, dengan diketahui titik-titik koordinat berikut ini!

a. A (–5 : 2) & B (5 : 6)

b. A (3 : –5) & B (8 : 9)

Jawab

a. A (–5 : 2) & B (5 : 6)

∆Y Y₂ – Y₁ 6 – 2 4 4 2

b = —— = ————— = ————— = ————— = —— = —

∆X X₂ – X₁ 5 – (– 5) 5 + 5 10 5

b. A (3 : –5) & B (8 : 9)

∆Y Y₂ – Y₁ 9 – (–5) 9 + 5 14 4

b = —— = ————— = ————— = ————— = —— = 2 —

∆X X₂ – X₁ 8 – 3 5 5 5

4. fungsi permintaan sebuah barang di tunjukan oleh perusahaan Q = 75 – 3P

a.

b. Q = 75 – 3P

If, Q = 10

Q = 75 – 3 (10)

Q = 75 – 30

Q = 45

c. Q = 75 – 3P

If, P = 0

Q = 75 – 3 (0)

Q = 75 – 0

Q = 75

d. Q = 75 – 3P

If, Q = 15

Q = 75 – 3P

15 = 75 – 3P

15 – 75 = – 3P

– 60 = – 3

60

P = — = 20

3

e. Q = 75 – 3P

If, Q = 0

Q = 75 – 3P

0 = 75 – 3P

–75 = –3P

P = 25

5. dik : P₁ = 5000

Q₁ = 30 orang

P₂ = 8000

Q₂ = 10 orang

Q₁ = a – bp

Q₂ = a – bp

Penyelesaian

a. Q₁ = a – bp

30 = a – 5000 b

Q₂ = a – bp

10 = a – 8000 b

30 = a – 5000 b

10 = a – 8000 b

———————— –

20 = 3000 b

20 1

b = —— = 0,007 / —

3000 150

Jadi, Q₁ = a – bp

1

30 = a – 0,007 (5000) / ( — x 5000 )

50

30 = a – 33,3

30 + 33,3 = a

63,3 = a

Fungsinya: Q = a – bp

1

Q = 63,3 – 0,007p / 63,3 – — p

50

Untuk Q2 & P2

Q₂ = a – bp₂

10 = a – 8000 b

b. kurvanya

jika Q = 0

Q = 63,3 –