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Homework Help: Hard graph !

  1. Mar 7, 2012 #1
    http://im16.gulfup.com/2012-03-07/1331125411751.png [Broken]

    I know the answer is (E) , but HOW ?
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Mar 7, 2012 #2


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    Are you sure it's meant to be E) because I'm getting D) :frown:

    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 y-x and the horizontal x+y so let Y=y-x and X=x+y and then rearrange the equation to make y the subject.
  4. Mar 7, 2012 #3
    Sorry,I'm not sure that the correct answer is (E) :(
  5. Mar 7, 2012 #4


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    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 :wink:
  6. Mar 7, 2012 #5


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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, (1-k)y= (1+k)x or y= (1+k)/(1-k) x. From the picture it appears that k is larger than 1 (the angle is greater than 45 degrees) so 1-k is negative. That, in turn, means that the fraction (1+k)/(1-k) is negative so the graph goes downward to the right. It also follows that k< -1.
  7. Mar 7, 2012 #6
    I didn't understand !

    Can you explain it more simply ?
  8. Mar 7, 2012 #7


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    Can you follow the procedure I outlined for you in post #2?
  9. Mar 7, 2012 #8
    Since the line passes throught the origin, and the slope builds an angle between 45 and 90 degrees, I can say that:
    y - x = a ( y + x), \ a > 1

    Solve this for y. What do you get?
  10. Mar 8, 2012 #9

    y(1-a)= x(1+a)

    so .. ?

  11. Mar 8, 2012 #10


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    Solve for y.

    Plug-in some positive numbers greater than 1, for a.

    BTW: Mentallic is right about what's the correct answer .
  12. Mar 10, 2012 #11


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    That graph in the picture appears to have a slope of about 3, for each mm horizontally it rises about 3mm, roughly (and assuming the scales are the same).

    Usually we would express that graph as being the plot: y = 3x

    But on this particular graph, the vertical quantity is given as y-x
    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.
  13. Mar 13, 2012 #12


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    Thread locked pending moderation.
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