Identify direct and inverse variation EXAMPLE 1 Tell whether the equation represents direct variation, inverse variation, or neither. a. xy = 4 SOLUTION.

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

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

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

GUIDED PRACTICE for Example 1 Tell whether the equation represents direct variation, inverse variation, or neither. 1. y = 2x2x ANSWER inverse variation

GUIDED PRACTICE for Example y = 3x ANSWER direct variation

GUIDED PRACTICE for Example x – y = 3 ANSWER neither

GUIDED PRACTICE for Example 1 4. xy = 1212 ANSWER inverse variation