In this section, tables are analyzed to determine if they represent an inverse variation.

The table below represents a relationship that is an inverse variation. Multiply the values for x and y together in each column. Use the link beneath the table to check your answer.

Example

x	2	3	4
y	6	4	3
Process	2 × 6 = ___	3 × 4 = ___	4 × 3 = ___

Interactive popup. Assistance may be required. Check Your Answer

2×6=12
3×4=12
4×3=12

• What do you notice about the products xy for each pair of numbers?

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  Check Your Answer

  The products are the same, and they are 12 each time.

The table below represents a relationship that is NOT an inverse variation. Multiply the values for x and y together in each column. Use the link beneath the table to check your answer.

x	2	3	4
y	4	6	8
Process	2 × 4 = ___	3 × 6 = ___	4 × 8 = ___

Check Your Answer

2×4=8
3×6=18
4×8=32

• What do you notice about the products xy for each pair of numbers?

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  Check Your Answer

  The products are different.

Pause and Reflect

If a relationship between x and y is an inverse variation, what can you say about the product of each pair of numbers xy?

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Check Your Answer

If a relationship is an inverse variation, the product xy will be the same for each pair of numbers x and y.

A constant product for an inverse variation is also called the constant of proportionality, k. How are k and the product xy related?

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Check Your Answer

xy = k.