Final answer:
The equation in the form y = kx to represent the number of products, y, produced in x hours of work at the factory is y = 80x, where k equals 80, indicating 80 products are produced each hour.
Step-by-step explanation:
The student is asking for an equation in the form y = kx to represent the relationship between the number of products produced, y, and the number of hours worked, x, in a factory setting.
To find the constant of proportionality k, we divide the total number of products by the total number of hours. In this case, the factory produces 640 products in 8 hours, so k is 640 / 8 which equals 80. Therefore, the equation that represents this situation is y = 80x.