3. Kate is planning on going to the pool a lot this summer. It costs $5 to go each time, but Kate noticed that the pool also offers a Summer Discount Card and a Summer Flat Rate Card. The Discount card costs $50 but would allow her to go to the pool for only $2 each time. The Flat Rate card costs $200 but would let her in to the pool for free all summer. a. What factors will be most important when Kate is deciding to buy the Discount card, the Flat Rate card, or neither? b. Write an equation for each of the three scenarios. Explain your thinking. c. Graph your equations in a graphing utility or in a calculator. What does the x-axis represent? What does the y-axis represent? d. What do the intersection points of the lines represent? e. Decide which plan you think is the best and explain why.