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## #1 2006-06-14 02:40:15

ketaciturn
Member
Registered: 2006-06-14
Posts: 2

### Get equation from graph

Hi..I am new to this forum n feel like this forum is real cool.. I have a question for u guys,

How can we actually obtain a equation from graph? For example, a sin(x) graph, if we dunno it is sin(x), how can we derive a equation by the value and coordinate on the graph?

Cheers
Jeff

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## #2 2006-06-14 02:57:49

ganesh
Registered: 2005-06-28
Posts: 23,771

### Re: Get equation from graph

Hi ketaciturn/Jeff,

I would say the easiest way to obtain the equation from the graphs is
find any two pairs of coordinates (x1,y1), (x2,y2),
that is find y1 from the graph for any value of x1, similarly find y2 from the graph for any value of x2.
Apply this formula for getting the equation of the straight line.

Remember, this would be applicable only for equations of straight lines, not curves.
In the alternative, if the angle made by the straight line with the positive x-axis is know, say θ, then the slope of the line is given by
m=tan θ.
Find any point y1 for a given x1, then use the following formula to get the  equation of the straight line.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #3 2006-06-14 03:11:23

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Get equation from graph

That works great for lines, but I believe (s)he wants all graphs.

The thing is, that while there are a finite amount of types of(known) "natural" graphs, such as sin or x^2, there are an infinite amount of unnatural graphs, such as the anti-derivative of e^(x^2).

To make matters worse, there is no method of finding a graph.  You must look at a graph, and see if it looks familiar to you.  Making a chart can help, but mostly, it's just recognition.  If I see a big U as a graph, my mind first thinks x^3.  Similarly, if I see a curvy line that goes on forever, I think it must be some trig function.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #4 2006-06-14 03:42:13

ketaciturn
Member
Registered: 2006-06-14
Posts: 2

### Re: Get equation from graph

would say the easiest way to obtain the equation from the graphs is
find any two pairs of coordinates (x1,y1), (x2,y2),
that is find y1 from the graph for any value of x1, similarly find y2 from the graph for any value of x2.
Apply this formula for getting the equation of the straight line.

Remember, this would be applicable only for equations of straight lines, not curves.
In the alternative, if the angle made by the straight line with the positive x-axis is know, say θ, then the slope of the line is given by
m=tan θ.
Find any point y1 for a given x1, then use the following formula to get the  equation of the straight line.

That works great for lines, but I believe (s)he wants all graphs.

u r right. What I am looking for is a way to find a equation from all graphs (curves especially).

Thanks for both ganesh & ricky reply. But I still hoping for any suggestions..

Cheers
Jeff

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## #5 2006-06-14 04:21:42

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Get equation from graph

Are your graphs on paper or scanned into a computer, or computer generated, or made by data, or random, or what?
There may be programs to estimate your graph.  Equation fitting?  Curve fitting?

igloo myrtilles fourmis

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## #6 2006-06-14 09:19:39

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Get equation from graph

To curve fit well, you must know the parent curve.  But once you know the parent curve, finding the exact equation is just a matter of plugging in points, if you have them.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #7 2006-06-14 11:42:46

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### Re: Get equation from graph

In practice, when a scientist or resercher plots some data they collected, they simply take an "educated guess" about what the underlying function might be.

This guess is based on an understanding of the mathematics involved (maybe they know it should be "cyclical" and so expect a sine curve).

Sometimes the data doesn't behave according to "how it should" and this can lead to new discoveries (for example, the curve may be cyclical AND rising, so they want to know why it is rising).

In general, it is up to the human to look at the curve and "recognise" it.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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