Inverse Variation

Definition of Inverse Variation

  • Inverse variation is a variation in which the variable y varies inversely as x, if there is a nonzero constant k such that xy = k or , where .

Examples of Inverse Variation

  • The equations xy = 11, are examples of inverse variation.

More about Inverse Variation

  • In inverse variation, when one variable increases the other decreases in proportion so that the product remains the same always.


Solved Example on Inverse Variation

Determine whether the following statement is true.

If (r, a) and (v, f) both satisfy inverse variation, then    


A. yes

B. no                                                                           

Correct Answer: A

Step 1: The formula for an inverse variation is xy = k, where .

Step 2: Substitute (r, a) in the equation.

Step 3: ra = k

Step 4: Substitute (v, f) in the equation.

Step 5: vf = k

Step 6: So, ra = vf

Step 7:                 [Divide throughout by v.]

Step 8:                   [Divide throughout by a.]

Step 9: So, the given statement is true.

Related Terms for Inverse Variation

  • Constant
  • Variation


Additional Links for Inverse Variation