Tentukan rumus fungsi f(x) jika f(x) melalui titik (2/3,5) dan (-3/4,1/5)

Misalkan fungsinya linier
maka

ax + b = y

titik (⅔,5)
⅔a+b=5 ===> 2a+3b=15

titik (-¾,1/5)
-¾a+b=1/5 ===> -15a+20b=4

eliminasi a
pers1 × 15 ====> 30a+45b=225
pers2 ×2 ====> -30a+40b=8
______________________ +
============> 85b = 233
============> b= 233/85
2a+3b=15
2a=15-3b=15-3×233/85
= 1275/85 – 699/85
= 586/85

maka f(x) = 1/85 × (586x+233)

f(x)= ax+b

>> 2/3a+b= 5

>> -3/4a+b= 1/5

———————— (-)

2/3a + 3/4a= 24/5

17/12a= 24/5

a= 24/5 x 12/17

a= 288/85 . . . (1)

2/3a+b= 5

2/3 (288/85) +b= 5

2(96/85) +b= 5

192/85+b= 5

b= 5 – 192/85

b= 425/85 – 192/85

b= 233/85 . . . (2)

f(x)= ax+b

y= 288/85x + 233/85

——————————— (x85)

85y= 288x + 233

Jadi, 288x – 85y + 233 = 0

Semoga bermanfaat ya !