Final answer:
The equation that represents a direct variation is A. y = 15x, where the constant of variation is 15, indicating that y is directly proportional to x.
Explanation:Understanding Direct Variation
The concept of direct variation in mathematics is used to describe a relationship between two variables in which one is a constant multiple of the other. This relationship is expressed as y = kx, where k is the constant of variation, and it represents the slope of the line. Looking at the given options, the equation that represents a direct variation is A. y = 15x. Here, the constant of variation is 15, which means for every unit increase in x, y increases by 15 units.
The other options do not fit the definition of direct variation because they do not show a relationship where y is directly proportional to x. For instance, y is not expressed in terms of x at all in options B and C, and option D shows a relationship that is not a simple multiple of x. Therefore, those cannot represent direct variation.
Understanding direct variation is crucial for solving problems related to linear relationships where the rate of change between variables remains constant.