Slopes and equations of lines. must sow all work including 2 graphs for problem one (can use excel)

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  1. Graph the following equations. Make sure you clearly show the x and y intercepts on your graph.
    1. Graph:
      (2/3)x = 4 + y
    2. Graph:
      -3y + 12x = 15
  2. Answer the following questions pertaining to the following graph.
    1. Give a brief explanation describing the graph in terms of its x-axis and y-axis.
    2. At what age was the number of hours of television watched the least?
    3. Find the slope of the line. Show all work to receive full credit.
    4. Find the equation of the line that represents the number of hours of television watched. Show all work to receive full credit.
    5. What would the slope of the line be if 20-year-olds only watched 15 hours of television?
  3. The equation C = 5x + 300 represents the total cost to run Johnny’s Pizza place for a day. C symbolizes the total cost to open the pizza place, and x stands for the number of pizzas sold.
    1. Find the y-intercept of this graph and explain what it means in the context of the problem. Show all work to receive full credit.
    2. Explain the slope of the line within the context of this problem.
    3. What is C if 150 pizzas are sold in one day?
    4. Graph the equation.
  4. The director of a summer day camp estimates that 100 children will join if the camp fee is $350, but for each $20 decrease in the fee, 10 more children will enroll.
    1. Determine the linear equation that will represent the number of children who will enroll at a given fee. Hint: To write the slope, you need 2 points on the line. Show all work to receive full credit.
    2. Graph the linear equation that represents the number of children who will enroll at a given fee. Plot the number of children on the y-axis and the fee on the x-axis.
    3. Approximately how many students will enroll if the camp fee is $160? Round to the nearest child. Show all work for full credit.
    4. Approximately how many students will enroll if the camp is free? Round to the nearest child. Show all work for full credit?

  5. The number of arrests, y, of a city over a period of time, x, is graphed on a rectangular coordinate system.

    Write a paragraph describing your interpretation when the slope is positive, 0, and negative. If you were buying a home in this particular city, which slope would be most attractive to you, and why?

 
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