What does the eqn xy=k represent?
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 highschool, 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.
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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