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I cant figure this out indecision

 Jun 29, 2022
 #1
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When x changes by  3, y changes by   (13 - a)

 

From  4 to 13   x changes by 9  so  y changes by  3 (13 - a)=   39 - 3a

 

And  notice that

 

39 - 3a =  b   rearrange   as

 

3a + b =  39 

 

 

cool cool cool

 Jun 29, 2022
 #2
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0

The function, g or k ? is linear, so its graph will be a straight line, in which case the gradient between x = 1 and x = 4  will be the same  as that between x = 4 and x = 13.

So,

\(\displaystyle \frac{b-13}{13-4}=\frac{13-a}{4-1}.\)

From that,

\(\displaystyle 3b-39=117-9a,\\ 9a+3b=156, \\ 3a + b = 52.\)

 

Alternatively, let the equation of the function be \(\displaystyle f(x) = Ax + B.\)

Substituting the co-ordinates of the three points, we have

\(\displaystyle a = A+B, \dots(1) \\13=4A+B, \dots(2) \\ b = 13A+B, \dots (3)\)

from which,

\(\displaystyle 3a+b = 3(A+B)+(13A+B)=16A+4B=4(4A+B)=52.\)

 Jun 30, 2022

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