Final answer:
The correct equation representing a proportional relationship is B. Y=30x, as it is the only option without a y-intercept and follows the y = kx form, where k is the constant of proportionality.
Step-by-step explanation:
The question asks us to write the equation that represents a proportional relationship. A proportional relationship between two variables means that one variable is always a constant multiple of the other. Proportional relationships have equations of the form y = kx, where k is the constant of proportionality, and there is no y-intercept (b term) in the equation since the line must pass through the origin (0,0) for the relationship to be proportional.
Looking at the provided options, the only equation that fits this description is B. Y=30x. Equations A, C, and D involve either a different multiplier or an additional constant term (y-intercept), which would not represent a proportional relationship. Therefore, the correct equation that represents a proportional relationship is Y=30x.
By understanding the nature of a proportional relationship, it becomes clear that the presence of a constant addition or subtraction (the y-intercept) would disrupt the proportionality. Proportionality implies that for every unit increase in x, y increases by a fixed amount (the constant of proportionality). This relationship is evident in a graph where such an equation creates a straight line that goes through the origin, indicating that when x is 0, y is also 0.