Plants do eat food. They get the food through a process called photosynthesis. In this process, plants take carbon dioxide (the air we breathe out), water, and other nutrients, then uses sunlight to cocmbine these to make sugar. (The sunlight is captured and stored within an organ only plants contain called chloroplasts).
Animals get energy by eating food. Plants get energy through photosynthesis, the process when plants turn sun into energy.
Plants can make their own food through photosynthesis, while animals must consume food to obtain energy and nutrients. This difference classifies plants as autotrophs and animals as heterotrophs. The energy from food that animals consume comes from the organic compounds they rely on for survival.
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