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On the Graph, For How Many Values of x Does y=x?

  1. Apr 29, 2008 #1

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    1. The problem statement, all variables and given/known data

    On the graph, for how many values of x does y=x?


    2. Relevant equations


    3. The attempt at a solution

    The obvious answer is (0,0).
    There have to be more. I don't know how to go about finding this answer.
     

    Attached Files:

  2. jcsd
  3. Apr 29, 2008 #2
    If x is 10 can you give me a y such that y = x? If so thats the point (10,y)

    If x is 12.3 can you give me a y such that y = x? If so thats the point (12.3,y)

    If x is any value can you give me a y such that y = x? If so thats the point (x,y)

    Do you see the solution now?
     
  4. Apr 29, 2008 #3

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    I don't think so. Would the answer be all of them?

    Is there a specific number?

    I'm sorry. It's just not clicking.
     
  5. Apr 29, 2008 #4
    I'm sorry, I didn't see that there was an attachment. I thought your question was a bit easier. Your attachment awaits approval, can you describe it for me?
     
  6. Apr 29, 2008 #5

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    An "S" shape is plotted. The points above the graph are symmetrical to the points on the bottom. The only point that is labeled is (1,1). The very center of the "S" is at (0,0).

    At (1,1), (2,2) etc, y=x

    The possibilities are infinite.

    If I am on the right track, what would the answer be?

    An infinite number?
     
  7. Apr 29, 2008 #6
    No No. Again, I thought the question originally was how many points in the x,y plane does y = x. Of course the answer to that question is an infinite number. That however is not the question your were asking.

    To answer your real question, consider drawing the graph of the line y=x, through your S shape. Then the number of points at which it intersects your S is the number of values on your graph where y = x.

    Again, apologies for the confusion.
     
  8. Apr 29, 2008 #7

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    No worries. I probably didn't phrase it as best as I could have phrased it. I appreciate the help.

    If I did it correctly, There are 2 points that touch the "S" on each line. I drew lines at (1,1), (2,2), etc and at (0,0).

    At 0, there are 3.

    I don't know what the actual number is though. I'm still confused.
     
  9. Apr 29, 2008 #8

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    You've certainly got me confused! What lines did you draw at (1,1), (2,2), etc.?
    I have no idea what you are talking about when you say "At 0, there are 3"! What do you mean "at 0"? Do you mean "at (0,0)" or "at x= 0" or "at y=0"? And there are 3 what?

    The problem is asking "where does this graph cross the line y= x?" That's difficult to answer here because it depends strongly on how accurate this graph is supposed to be and exactly where each end of the "S" ends. Can you draw the line y= x?
     
  10. Apr 29, 2008 #9

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    Yes, at (0,0)

    I don't understand what you mean by the line y=x. I don't know where to draw it, or how/why it's just one line.

    I am sorry to confuse you. Things get lost in translation in this format.

    I'm not getting the concept but I am trying hard.
     
  11. Apr 29, 2008 #10
    The line y = x consists of all the points where *drumroll...* y = x. For example, (0, 0), (1, 1), (2.439, 2.439), etc. Plot two of these points on the graph (maybe (0, 0) and (1, 1) ). The straight line that connects these points is y = x. It extends out infinitely past both points.
     
  12. Apr 29, 2008 #11

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    I sort of understand that. But I still don't understand what the answer is.

    How many are there? It seems that the number is infinite.
     
  13. Apr 29, 2008 #12
    The number of points on the line y = x is infinite, but the number of points where the line y = x intersects your "S" is not. Draw the line y = x as well as the "S," and the points where the lines cross will be the intersection points.

    For example, in this graph, there are two points where the line intersects the ellipse.
     
  14. Apr 29, 2008 #13

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    3?

    I don't think that I am drawing y=x correctly.
     
  15. Apr 29, 2008 #14
    y=x is a straight line, at an elevation of 45 degrees from the x-axis, working counterclockwise. Plot that, and the answer will be however many times that graph and the line intersect.
     
  16. Apr 29, 2008 #15

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    I came up with 2.
     
  17. Apr 29, 2008 #16

    HallsofIvy

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    Good! How did you come up with that? I presume you have a clearer picture than we can see on the internet, because I was not at all sure. (Of course, I didn't want to draw on my computer screen!) Obviously, as you said, (0,0) is one point of intersection. Is the other in the lower left (3rd quadrant) or upper right (1st quadrant)?
     
  18. Apr 29, 2008 #17

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    Would you believe on a wing and a prayer?

    Wow, I actually got the answer? Finally!?!?!?
    2, 2, 2, 2, 2, 2....!!!!!!

    Upper right?
     
  19. Apr 29, 2008 #18
    If you look at the graph (the image has finally been approved), you will see that the origin and also the two end points of the S all lie on the line y = x, so there are actually 3 points that the line y = x intersects. The end points of that graph should really be labeled, though.
     
  20. Apr 29, 2008 #19

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    It's all I have. It might have been easier had the graph been better.

    Thanx again

    :)
     
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