Final answer:
The correct equation to represent the scenario where Katerina ran 1/2 more miles than Jackson is y = (3/2)x. This equation shows that Katerina ran 1.5 times the distance that Jackson did, which fits the given situation.
Step-by-step explanation:
The student is asking for help in finding the equation that represents the situation where Katerina ran 1/2 more miles than Jackson, if Jackson ran x miles. To model this situation, we need an equation that takes Jackson's distance x and adds half of that distance to it, which is represented mathematically as x + (1/2)x, which simplifies to (3/2)x. Therefore, the correct equation that represents the distance Katerina ran, given the symbol y for her distance in miles, is y = (3/2)x.
The first option in the list of equations, y = (3/2)x, correctly expresses this relationship, as it indicates that Katerina ran three halves, or 1.5 times, the distance that Jackson ran. The relevance of the linear equation is that it establishes a proportional relationship between Jackson's and Katerina's distances ran, which fits the description of the scenario provided by the student.