Final answer:
The process responsible for eutrophication in the water cycle when farmers use pesticides and fertilizer is run-off.
Step-by-step explanation:
The process in the water cycle responsible for eutrophication when farmers on mountainsides use pesticides and fertilizer, and the runoff enters rivers, lakes, and oceans is run-off. When farmers use pesticides and fertilizers, these substances can be washed away by rainwater or snowmelt and enter nearby water bodies. This runoff can introduce high concentrations of nutrients, such as phosphates and nitrates, into the water, promoting the growth of algae and microorganisms. The excessive growth of algae and microorganisms can lead to eutrophication, which negatively affects water quality and can harm aquatic life.