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Hard graph !by ABC_123
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#1
Mar712, 07:07 AM

P: 5

I know the answer is (E) , but HOW ? 


#2
Mar712, 07:28 AM

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Are you sure it's meant to be E) because I'm getting D)
If you were given a linear graph with the vertical axis being Y, and the horizontal being X, then you could say that Y=mX for some constant m, right? You can similarly substitute each axis representation into this equation. The vertical is now yx and the horizontal x+y so let Y=yx and X=x+y and then rearrange the equation to make y the subject. 


#3
Mar712, 07:34 AM

P: 5

Sorry,I'm not sure that the correct answer is (E) :(



#4
Mar712, 08:28 AM

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Hard graph !
No worries. On the other hand, I'm quite sure the answer is D, but it doesn't even matter, we should just let the math do the talking



#5
Mar712, 08:46 AM

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The first graph is a straight line passing through the origin so it must be of the form y x= k(x+ y). That is the same as y x= kx+ ky or y ky= x+ kx. Factoring, (1k)y= (1+k)x or y= (1+k)/(1k) x. From the picture it appears that k is larger than 1 (the angle is greater than 45 degrees) so 1k is negative. That, in turn, means that the fraction (1+k)/(1k) is negative so the graph goes downward to the right. It also follows that k< 1.



#6
Mar712, 10:02 AM

P: 5

I didn't understand !
:( Can you explain it more simply ? 


#7
Mar712, 08:32 PM

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Can you follow the procedure I outlined for you in post #2?



#8
Mar712, 08:52 PM

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Since the line passes throught the origin, and the slope builds an angle between 45 and 90 degrees, I can say that:
[tex] y  x = a ( y + x), \ a > 1 [/tex] Solve this for y. What do you get? 


#9
Mar812, 08:17 AM

P: 5

y(1a)= x(1+a)
so .. ? 


#10
Mar812, 09:31 AM

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Plugin some positive numbers greater than 1, for a. BTW: Mentallic is right about what's the correct answer . 


#11
Mar1012, 06:37 AM

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Usually we would express that graph as being the plot: y = 3x But on this particular graph, the vertical quantity is given as yx and the variable on the horizontal is given as y+x So substitute these expressions for the y and x in the blue equation, respectively. Finally, rearrange the result to get y on one side by itself. 


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