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## 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.

• 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

Choices:

A. yes

B. no

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