Final answer:
The equation that represents a proportional relationship is y = 3x, which is in the direct variation form of y = kx and implies a constant rate of change without a y-intercept.
Step-by-step explanation:
The equation that represents a proportional relationship is the one that can be expressed in the form y = kx, where k is a constant. Proportional relationships imply a direct variation between two variables, meaning as one variable increases, the other variable changes at a constant rate. A pure proportional relationship will pass through the origin (0; 0), so it should not have a constant term (no y-intercept).
Looking at the provided equations:
- y = -3x + 2 is not proportional since it has a y-intercept of 2.
- y = 2/7 is not a variable equation but a constant value, thus not proportional.
- y = 2(x + 1) also has a y-intercept and is not a direct variation.
- y = 3x perfectly fits the definition of proportional relationship as it is in the form y = kx with k = 3, and passes through the origin.
Therefore, the equation y = 3x represents a proportional relationship.