EXAMPLE 1 Identify direct variation equations

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EXAMPLE 1 Identify direct variation equations Tell whether the equation represents direct variation. If so, identify the constant of variation. 2x – 3y = 0 a. –x + y = 4 b.

Identify direct variation equations EXAMPLE 1 Identify direct variation equations SOLUTION To tell whether an equation represents direct variation, try to rewrite the equation in the form y = ax. 2x – 3y = 0 Write original equation. –3y = –2x Subtract 2x from each side. y = 2 3 x Simplify. ANSWER Because the equation 2x – 3y = 0 can be rewritten in the form y = ax, it represents direct variation. The constant of variation is . 2 3

Identify direct variation equations EXAMPLE 1 Identify direct variation equations b. –x + y = 4 Write original equation. y = x + 4 Add x to each side. ANSWER Because the equation –x + y = 4 cannot be rewritten in the form y = ax, it does not represent direct variation.

GUIDED PRACTICE for Example 1 Tell whether the equation represents direct variation. If so, identify the constant of variation. 1. –x + y = 1 ANSWER not direct variation

GUIDED PRACTICE for Example 1 Tell whether the equation represents direct variation. If so, identify the constant of variation. 2. 2x + y = 0 ANSWER direct variation; –2

GUIDED PRACTICE for Example 1 Tell whether the equation represents direct variation. If so, identify the constant of variation. 3. 4x – 5y = 0 ANSWER direct variation; 4 5