(Originais Teachy 2023) - Question Very Hard of Mathematics

A company that manufactures parts for automobiles observed that the monthly production cost of a certain item varies according to the quantity produced. They collected the following data over two months of production: in the first month, when they produced 200 items, the production cost was R$ 4000.00, and in the second month, when they produced 400 items, the cost was R$ 7000.00. Considering that the production cost can be modeled by a first-degree function, which is represented by a line in the Cartesian plane, and that the production cost is directly proportional to the quantity of items produced, determine the function that best represents the monthly production cost of these items. Then, based on the found function, estimate the production cost for 600 items in the third month of production.