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"We reviewed the student's homework. She was to graph, by hand, the profit-yielding equation (P = 11.43a - 1,425,000), which relates the number of festival attendees to a particular amount of profit in $USD. First, we estimated aspects of it (Where does it cross the y-axis? What's the approximate angle of the straight line created by it?), and then we graphed the line more accurately. We also talked about the "break-even" point, and how it related to profit, and attendees. We also first estimated it by simply viewing the graph, and then algebraically solving the equation to find the precise break-even point, and what that really meant (expenses = income, profit = $0, and at that point, a certain number of attendees would have actually bought tickets, which tells a CEO that more attendees need to be recruited to the event if the operation is to have a successful return for investors). Next, we solved and graphed a set of two equations to see where they intersect, and began discussions about what this actually means, and how it can relate to real life (for example, in a similar situation involving the last business situation). She understood this concept immediately, and her homework was to, 1. estimate where the two lines intersect, 2. find the precise point at which they intersect, and 3. explain what significance the intersection has on both lines (equations), and to extend that to a real-life scenario."