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Recognizing Direct and Inverse Variation Equations

Learn to identify direct and inverse variation in equations, determine the type of variation represented, and practice with examples. Understand the concepts of constants of variation and how they relate to the equations given.

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Recognizing Direct and Inverse Variation Equations

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  1. Because xy = 4 can be written in the form y =, xy = 4 represents inverse variation. The constant of variation is 4. a x y = 4 x EXAMPLE 1 Identify direct and inverse variation Tell whether the equation represents direct variation, inverse variation, or neither. a. xy = 4 SOLUTION xy = 4 Write original equation. Divide each side by x.

  2. = x b. = x y y y 2 y 2 2 Because= xcan be written in the formy = ax, = x represents direct variation. 2 EXAMPLE 1 Identify direct and inverse variation Tell whether the equation represents direct variation, inverse variation, or neither. SOLUTION Write original equation. y = 2x Multiply each side by 2.

  3. Because y = 2x + 3cannot be written in the formy = or y =ax, y = 2x + 3 does not represent either direct variation or inverse variation. a x EXAMPLE 1 Identify direct and inverse variation Tell whether the equation represents direct variation, inverse variation, or neither. c.y = 2x + 3 SOLUTION

  4. 2x ANSWER inverse variation for Example 1 GUIDED PRACTICE Tell whether the equation represents direct variation, inverse variation, or neither. 1.y =

  5. ANSWER direct variation for Example 1 GUIDED PRACTICE 2. 4y = 3x

  6. ANSWER neither for Example 1 GUIDED PRACTICE 3. 5x – y = 3

  7. 12 ANSWER inverse variation for Example 1 GUIDED PRACTICE 4. xy =

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