What does the equation xy=k represent?

  • Context: High School 
  • Thread starter Thread starter svigneshkumars
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the interpretation of the equation xy=k, exploring its implications in various contexts such as functions, graphing, and mathematical relationships. Participants examine the meanings of the variables involved and the resulting graphical representations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that the interpretation of the symbols x, y, and k is crucial to understanding the equation.
  • One participant proposes that the equation can represent a function f(x, y) = k, where k is the output of the multiplication of x and y.
  • Another participant notes that solving the equation for y yields y = k/x, indicating an inverse variation.
  • It is mentioned that if x and y are treated as variables and k as a constant, the graph of the equation will depict a hyperbola.
  • One participant introduces the idea that if "xy" is considered a constant, the graph could represent a straight line in a (k,l)-coordinate system.

Areas of Agreement / Disagreement

Participants express differing interpretations of the equation, with no consensus on a single meaning or representation. Multiple competing views remain regarding the nature of the graph and the roles of the variables.

Contextual Notes

The discussion highlights the dependence on the definitions of the variables and the assumptions made about their relationships. There are unresolved aspects regarding the specific contexts in which the equation is applied.

Who May Find This Useful

This discussion may be of interest to those exploring mathematical functions, graphing techniques, or the relationships between variables in algebraic equations.

svigneshkumars
Messages
10
Reaction score
0
What does the eqn xy=k represent?
 
Mathematics news on Phys.org


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.
 

Similar threads

High School Adding 'x' to 'xy' for Resultant <=1: A Table Guide
  • · Replies 18 ·
Replies
18
Views
3K
High School Is PI (##\pi##) really a number?
  • · Replies 28 ·
Replies
28
Views
3K
High School Imaginary Pythagoras
  • · Replies 13 ·
Replies
13
Views
2K
High School What is a closed form solution?
  • · Replies 1 ·
Replies
1
Views
2K
What does a row matrix represent geometrically?
  • · Replies 8 ·
Replies
8
Views
1K
High School What is this part of a graph on the axis called?
  • · Replies 7 ·
Replies
7
Views
20K
MHB 71 Under what conditions does the ratio A}/B equal A_x//B_x
  • · Replies 2 ·
Replies
2
Views
1K
High School Can anyone tell me how the graph would be if the equation is XY=K(K is
  • · Replies 1 ·
Replies
1
Views
2K
High School What went wrong with (-x)^2=x^2?
  • · Replies 22 ·
Replies
22
Views
3K
High School Complicated equation and Simple equation for the Same Curve?
  • · Replies 49 ·
2
Replies
49
Views
4K