What does the equation xy=k represent?

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SUMMARY

The equation xy=k represents a relationship where x and y are variables and k is a constant. This equation can be interpreted as a function f(x, y) = k, where the output k is the product of the inputs x and y. When solved for y, the equation becomes y = k/x, indicating an inverse variation. Graphically, this relationship produces a hyperbola when plotted on a coordinate system, illustrating the dependency between the variables.

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What does the eqn xy=k represent?
 
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It depends upon the interpretation of your symbols x,y and k.
 


In many cases, that will represent a function (though I'm used to seeing z insteak of k.)
f(x, y) = k. In your case, f(x, y) takes the two inputs (x and y, obviously) and multiplies them together. k is called the output, x and y are inputs. Most people will remember seeing f(x) = y in high school, in this case f() has two variables intead of one. As Arlidno mentions, the interpretation will vary. x may represent height and y may represent width, hence k would represent the area of a square-ish object.
 


svigneshkumars said:
What does the eqn xy=k represent?

Well, if you solve it for y, then you get: y = k/x. This is an inverse variation.

It could be as simple as that.
 


Assuming x and y are variables and k is a constant, the graph will be a hyperbola.
 


Assuming "xy" is a constant, the k-graph is either a straight line, assuming a (k,l)-coordinate system to speak out from.
 

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