Final answer:
The correct equation to represent the number of widgets produced over a certain number of days by the factory is y = 5,000x. This is a direct relationship where each day yields 5,000 widgets, making it a linear equation with a slope of 5,000 and no y-intercept.
Step-by-step explanation:
The question involves finding an equation to represent the number of widgets produced over a certain number of days. Since the factory produces 5,000 widgets each day, the relationship between the number of widgets (y) and the number of days (x) is a direct multiplication. Therefore, for every day x, 5,000 widgets are produced. The correct equation expressing this relationship is y = 5,000x.
To clarify, if the factory operates for one day, it would produce 5,000 widgets (y = 5,000*1). If it operates for two days, it would produce 10,000 widgets (y = 5,000*2), and so on. This is a simple linear equation where the slope represents the production rate per day, and there is no y-intercept since there are no widgets produced at day zero.