Asif wants to open a lemonade stand during a town fair. He buys a pitcher and lemonade concentrate from a store for this purpose. At the lemonade stand, the cost for each cup of lemonade will be the same. If Asif sells 32 cups of lemonade, he will have a profit of $0. If he sells 45 cups of lemonade, he will have a profit of $16.25. Determine the rate of change for a function that represents Asif's profit, y, in dollars, from selling x cups of lemonade.

Explain what the rate of change from Part A indicates in terms of the context.

If a graph of the profit function is made, explain how the rate of change from Part A will be shown on the graph.

Make a conjecture about the initial value of the profit function. Prove or justify your conjecture.