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September 18th, 2016, 07:22 AM   #1
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formula to detect direct or inverse related values

Hello All

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

Basicaaly 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

I have seemed to find the answer BUT with trial and error
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


but is there a 'proper' way to get the formula( other than guesswork and unlike the un-structural method like I have done above) ?

Thanks in advance
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September 18th, 2016, 10:02 AM   #2
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some more :

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.

can anyone assist on how to crackt his in a structural way ?
Thanks,
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September 18th, 2016, 10:58 AM   #3
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the data has a constant rate of change ...

$\dfrac{\Delta y}{\Delta x} = \dfrac{11-1}{4-0} = \dfrac{5}{2}$

$\dfrac{\Delta y}{\Delta x} = \dfrac{31-11}{12-4} = \dfrac{5}{2}$

$\dfrac{\Delta y}{\Delta x} = \dfrac{71-31}{28-12} = \dfrac{5}{2}$

... x and y have a direct linear relationship

$y = \dfrac{5}{2}x+1$
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September 18th, 2016, 11:43 AM   #4
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Thanks. Issue is resolved.
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