My Math Forum formula to detect direct or inverse related values

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 September 18th, 2016, 07:22 AM #1 Member   Joined: Nov 2012 From: The Netherlands Posts: 40 Thanks: 2 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
 September 18th, 2016, 10:02 AM #2 Member   Joined: Nov 2012 From: The Netherlands Posts: 40 Thanks: 2 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,
 September 18th, 2016, 10:58 AM #3 Math Team     Joined: Jul 2011 From: Texas Posts: 2,924 Thanks: 1521 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 $y = \dfrac{5}{2}x+1$ Thanks from hello_math
 September 18th, 2016, 11:43 AM #4 Member   Joined: Nov 2012 From: The Netherlands Posts: 40 Thanks: 2 Thanks. Issue is resolved.

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