Formula to detect direct or inverse related values

[radaway]

Homework Statement

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[/B]

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

Homework Equations

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

 

[member 587159]

Are you given that $y(x)$ is a line (equation of degree $1$)? If not, are you familiar with systems of linear equations?

 

[radaway]

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 that's 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,

 

[member 587159]

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 that's 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,

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

Are you allowed to use a calculator or something?

 

[radaway]

yes a calculator is allowed. I have a casio fx-82es plus, but would not know how to

 

[SammyS]

Homework Statement

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[/B]

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

Homework Equations

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

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 ?

 

[radaway]

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')

 

[SammyS]

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

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 = y_n + (2.5)(x - x_n) ,
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.​

.

 

[radaway]

Thanks !