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# suatu fungsi dengan rumus f(x)=ax+b jika f(4)=5 dan f(-2)= -7 , maka tentuka rumus fungsi f(x)?

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suatu fungsi dengan rumus f(x)=ax+b jika f(4)=5 dan f(-2)= -7 , maka tentuka rumus fungsi f(x)?

Guest Apr 15, 2017
#2
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Translation......we wish to write the equation of a line in the form y = mx + b given the points (4, 5)  and (-2, -7)

First.....find the slope  =   [subtract y's in some order] / [ subtract x's in the same order]

So we have

[ -7 - 5] / [ -2 - 4]  =  -12/ -6    = 2

And using either point ....the point-slope form becomes

y = 2(x - 4) + 5  simplify

y = 2x - 8  + 5

y = 2x  - 3

CPhill  Apr 15, 2017
edited by CPhill  Apr 15, 2017
#3
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suatu fungsi dengan rumus f(x)=ax+b jika f(4)=5 dan f(-2)= -7 , maka tentuka rumus fungsi f(x)?

A function f(x) = ax + b.    If  f(4) = 5 and  f(-2) = -7, then the function is f(x) = ?

$$f (x) = ax + b$$

$$f (4) = a\cdot 4 + b=5$$

$$a=\frac{5-b}{4}$$

$$f (-2) = -2\cdot a + b=-7$$

$$a=\frac{-7-b}{-2}$$

$$\frac{-7-b}{-2}=\frac{5-b}{4}$$

$$-28-4b=2b-10$$

$$6b=-18\\\color{blue}b=-3$$

$$a=\frac{5-b}{4}\\a=\frac{5+3}{4}$$

$$a=2$$

$$\large f(x)=2x-3$$

! Thank you C.

asinus  Apr 15, 2017
edited by asinus  Apr 15, 2017
edited by asinus  Apr 15, 2017
edited by asinus  Apr 15, 2017
edited by asinus  Apr 15, 2017
#4
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Notice asinus, that  for  (4,5) , y =  -x + 9    is correct

But....for   (-2, - 7)    we have that   f(-2)  =  - (-2) + 9   =  11    which is incorrect

CPhill  Apr 15, 2017