Final answer:
The equation that represents direct variation among the options given is A. -2x = 3y, which can be rewritten in the form y = (-2/3)x.
Step-by-step explanation:
The question asks us to identify which equation represents direct variation. An equation represents direct variation when the ratio of the dependent variable (y) to the independent variable (x) is constant. This means the equation can be written in the form y = kx, where k is the constant of variation, and there is no y-intercept (a = 0).
In the options provided:
- A. -2x = 3y can be rewritten as y = -(2/3)x, which is a direct variation.
- B. 5y - x = 4 cannot be represented as y = kx because of the constant term.
- C. 12x - 3 = 4y cannot be represented as y = kx because of the constant term.
- D. 5x - 2y + 3 = 0 cannot be represented as y = kx because of the constant term.
Therefore, the equation that represents direct variation is A. -2x = 3y.