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Homework Help: General form of an equation with undefined slope

  1. Sep 3, 2017 #1
    1. The problem statement, all variables and given/known data
    The equation of the line that goes through the points 13b789c2c63f8667cc8318bdc8e9fb1.png and 712edb38d6ad41f4e48bc2c2f3f6661.png can be written in general form 0e069a9bedaddf294b9e0c6ef8663e1.png . What are the values for A, B, and C?

    2. Relevant equations
    Ax+By+C=0

    3. The attempt at a solution
    I think the answer is x=1. But how do i express that in general form?
     
    Last edited by a moderator: Sep 3, 2017
  2. jcsd
  3. Sep 3, 2017 #2

    Mark44

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    As x - 1 = 0.
    In this form, A = 1. Can you figure out what B and C are?
     
  4. Sep 3, 2017 #3
    The software says A=1 is wrong.
     
  5. Sep 3, 2017 #4
    I just found out how to do it. Pretend you're trying to figure out the slope. you get 4/0 . 4 is the value for A. 0 for B. solve for c.

    A= 4
    B= 0
    C= -4
     
  6. Sep 4, 2017 #5

    SammyS

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    Does the software mark A, B, and C individually or does it mark them together as a group of numbers ?
     
    Last edited: Sep 4, 2017
  7. Sep 4, 2017 #6
    Individually.
    A= blank. B=blank. C=blank
     
  8. Sep 4, 2017 #7
    I recommend reviewing post #2 to get the line in the given general form...
     
  9. Sep 4, 2017 #7

    SammyS

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    I take that the software says those answers are correct.

    As it turns out there are infinitely many correct solutions. (You might say, infinitely many.)

    The only one of the three which must have a particular value is B, which is zero.

    The only requirements on A and C is that A = −C , so that A + C = 0 .
     
  10. Sep 4, 2017 #8
    I am pretty sure at one point I had 1 and -1 for a and c and software marked it wrong. Grrrrrr.
     
  11. Sep 4, 2017 #9
    I plugged 4 in for A and 0 for B because I read somewhere you act like you're going to figure the slope out (even though you can't) in order to get A and B.
     
  12. Sep 4, 2017 #10

    Nidum

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    Rewrite the equation in slope and intercept form : y = mx + d

    Sketch the graph of the line .

    Is there something about the coordinate values given for those two points on the line that might cause you to think about this problem in a particular way ?
     
    Last edited: Sep 4, 2017
  13. Sep 4, 2017 #11

    SammyS

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    Using that same idea, you can just as well get A = −4, B = 0, and C = 4 , by using the coordinates in the reverse order.
     
  14. Sep 4, 2017 #12
    Yes. I see how infinitely many solutions are possible for a and c. I put the equation in
    Yes. I see you can put any number and its complement to make b 0. I also solved for x and got x=1 which makes sense. How would i get the equation for a vertical line at 2?
     
  15. Sep 4, 2017 #13
    They form a straight vertical line?
     
  16. Sep 4, 2017 #14
    Also, I converted it to slope intercept form. I get 0=-4x+4. Is that what you're getting at?
     
  17. Sep 4, 2017 #15
    Or simply y=-4x+4?
     
  18. Sep 4, 2017 #16

    SammyS

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    So you want an equation of the form ##\ Ax+By+C = 0\ ## that with suitable values for A, B, C is equivalent to the equation ##\ x=2\ .##

    ##\ x=2\ ##
    is equivalent to
    ##\ x-2=0\ .##
    Multiplying by A and adding ##\ 0y\ ## gives
    ##\ Ax+0y-2A=0\ .\ ## (Solve it for x to convince yourself.)

    So B = 0, and you can choose any non-zero number for A (you need x in the equation). Then C is −2 times the value chosen for A.

    Otherwise, to do it by your method:
    Pick any two distinct points, both having 2 for the x coordinate and proceed.
     
  19. Sep 4, 2017 #17

    epenguin

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    Now you have got what Nidum #10 hinted. You could have said at the start: to one x value corresponds two y values; for a straight line that can only be a vertical line.
    Sure you copied out the question right?
     
    Last edited: Sep 5, 2017
  20. Sep 4, 2017 #18
    I am sure I copied the question right. Thanks.
     
  21. Sep 4, 2017 #19

    epenguin

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    So in conclusion what is the equation of the line in simplest form?
     
  22. Sep 4, 2017 #20
    simplest form, I would say x=1. I am heeding what it says in your sig.
     
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