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A charity organization had to sell 1818 tickets to their fundraiser just to cover necessary production costs. They sold each ticket for $45\$45. Let yy represent the net profit (in dollars) when they have sold xx tickets. Which of the following information about the graph of the relationship is given?

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Q. A charity organization had to sell 1818 tickets to their fundraiser just to cover necessary production costs. They sold each ticket for $45\$45. Let yy represent the net profit (in dollars) when they have sold xx tickets. Which of the following information about the graph of the relationship is given?
  1. Establish Equation: To determine the relationship between the number of tickets sold xx and the net profit yy, we need to establish an equation that represents this relationship. We know that the charity organization needs to sell 1818 tickets at $45\$45 each to cover their production costs. This means that the break-even point is at 1818 tickets.
  2. Calculate Revenue: The total revenue from selling xx tickets is given by the equation Revenue=45x\text{Revenue} = 45x, since each ticket is sold for $45\$45.
  3. Determine Cost: The fixed production cost is the cost that the charity needs to cover by selling 1818 tickets. This cost is given by Cost=18×45\text{Cost} = 18 \times 45.
  4. Calculate Net Profit: To calculate the net profit yy, we subtract the fixed production cost from the total revenue. The net profit equation is y=45x(18×45)y = 45x - (18 \times 45).
  5. Simplify Equation: Simplifying the net profit equation, we get y=45x810y = 45x - 810.
  6. Graph Relationship: The graph of this relationship would be a straight line with a slope of 4545 and a yy-intercept of 810-810. The slope of 4545 indicates that for each additional ticket sold, the net profit increases by $45\$45. The yy-intercept of 810-810 indicates that if no tickets were sold, the organization would be at a loss of $810\$810, which corresponds to the production costs.

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