choosing x and y coordinates in a direct variation

Question

In direct variation is there any particular and unique method for selection of variables in x and y axis 

Answer 1

No.  

 

Direct variation means that Y = K*X for some constant K, so "Y varies directly with X" means that if X is increased (or decreased) by some number N then Y is increased (or decreased) by K*N.  But if you solve the equation for X you will find that X = (1/K)*Y, so X varies directly with Y as well, just with the constant of variation being (1/K) instead of K.  And you can check that if Y is increased (or decreased) by some number K*N then X will be increased (or decreased) by N.  So the 2 equations are just different forms of the same direct variation, you can use whichever one is more convenient.  

 

In theory X should represent the independent variable and Y should represent the dependent variable, but this is not always followed in practice.  I see plenty of problems on here where people are asked to determine the temperature T as a function of the number of cricket chirps C per hour, but clearly the temperature is not dependent on the number of cricket chirps!  When you have a linear relation it doesn't really matter which variable you put on which axis, the graph will just be rotated 90 degrees in one case versus the other.  So unless you are told which way specifically you can use either way.  

Answer 2

If the problem is worded "y varies directly as x," then whatever the y variable represents would go on the vertical axis.  The general equation is y = kx.

 

Another way to look at it is to determine

• which variable or quantity is considered the input or the independent variable--this would be x or the horizontal axis.
• which variable or quantity is considered (or acts like) the output or the dependent variable--this would be y or the vertical axis.