EXAMPLE 1 Identify direct variation equations Tell whether the equation represents direct variation. If so, identify the constant of variation. a. 2 x – 3 y = 0 b. –x + y = 4
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. 2 x – 3 y = 0 – 3 y = – 2 x 2 x y= 3 Write original equation. Subtract 2 x from each side. Simplify. ANSWER Because the equation 2 x – 3 y = 0 can be rewritten in the form y = ax, it represents direct variation. The constant of variation is 2. 3
EXAMPLE 1 b. Identify direct variation equations –x + y = 4 y = x+4 Write original equation. 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. 2 x + 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. 4 x – 5 y = 0 ANSWER direct variation; 4 5