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Formula to detect direct or inverse related values

  1. Sep 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Hello All

    via the following x, y values , a formula needs to be decided for the 'Y ' variable.

    Basicaly Consider the table below for x and y (are they directly proportional or are they inversely related ? ). and also to find out the corresponding formula. Pl. see the image


    http://s6.postimg.org/nph5u40dd/math.png

    2. Relevant equations


    3. The attempt at a solution
    It seems that I have bumped onto to the answer BUT with trial and error methods :p
    for e.g ( 4,11 :--> 4 X 2 = 8 +3) say this is 'Try 1'

    for ( 12,31 :---> 12 X 2 = 24 +7) and so on

    also in the (8+3) above , take the '3' & in (24+7) above take the '7' , which gives a pattern of 'multiply with 2' +1 (notice the '1')

    and when I would repeat the above once again but this time with
    for e.g ( 4,11 :---> 4 X 3 = 12) say this is 'Try 2'

    then I just take the (a gamble) of 'Try 1' and 'Try 2' and can settle for 2.5 as the factor :)

    so y = 2.5x + 1 is the formula ( or 5/2x +1)


    Question:

    Is there a 'proper' way to get the formula( other than guesswork and a not like the un-structural method like I have done above) ?

    Thanks in advance
     
    Last edited: Sep 18, 2016
  2. jcsd
  3. Sep 18, 2016 #2

    Math_QED

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    Are you given that ##y(x)## is a line (equation of degree ##1##)? If not, are you familiar with systems of linear equations?
     
  4. Sep 18, 2016 #3
    No this is not a straight line.{ (y = cx ), where c is a constant}
    neither is this of the format y = c/x or x = c/y
    i think its an odd one out ( maybe a hyperbola, or an asymptote ...not sure.)

    all thats given is what I have shown in the picture file. and the instruction is : get the formula...which I have but in a very unstructural manner.

    Thanks,
     
  5. Sep 18, 2016 #4

    Math_QED

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    You get ##y = 2,5x + 1## which is the equation of a line.

    Are you allowed to use a calculator or something?
     
  6. Sep 18, 2016 #5
    yes a calculator is allowed. I have a casio fx-82es plus, but would not know how to
     
  7. Sep 18, 2016 #6

    SammyS

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    Find the slope determined by the first two points.

    Find the slope determined by the second and third points. (It turns out to be the same as above.)

    Does the slope determined by points 3 and 4 match the above ?
     
  8. Sep 18, 2016 #7
    thanks that helped abit

    for the records: slope = change in Y/ chg. in x

    10/4, 20/8, 40/16 all amount to : 2.5 , the query now remains: where is the '1' coming from (2.5x +'1')
     
  9. Sep 18, 2016 #8

    SammyS

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    What is the y - intercept ?

    (In this case, it's right there in the table.)

    Otherwise, there are several methods.

    You know the form of the equation of a line with slope 2.5 is
    y = (2.5)x + b. ​
    Plug in x and y from one of the points in the table, and solve for b.

    Or use another form:
    y = yn + (2.5)(x - xn) ,
    where n = 1, 2, 3, or 4, signifying which point you use.
    If the points all fall on the same line, then they all give the same result when simplified.​
    .
     
  10. Sep 18, 2016 #9
    Thanks !
     
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