Name___________________________________________________ Applications of Graphing Homework Math 8 The Ohio Theater publishes a playbill for each play, which helps offset production costs. The playbill contains information and pictures of cast members as well as interviews with the producer and director. The owner of the theater must consider how much to charge for each playbill, and how much money can be raised. 1. The accountant for the production has researched previous years’ sales records and organized the results in the following table. Graph the data on the grid below. Theater Playbill Sales Number of Playbill Sold $2.50 1,625 $4.00 1,250 $5.00 1,000 $5.50 875 $7.50 375 2000 Number of playbills sold Playbill Price 2375 1500 1000 500 2. Draw a line through the points on your graph. 2 4 6 2 playbill2 price 8 2 3. The relationship between the price and the number of playbills sold is linear. Justify this statement using both the table and the graph. 4. Determine the slope of the line through the points. 5. Describe the meaning of the slope in this problem situation. 10 2 6. Use the data in the table and the graph to determine the y-intercept of the line through the data points. 7. Describe the meaning of the y-intercept in this problem situation. 8. Write the equation of the line through the data points in slope-intercept form. 9. Is the relationship between the price of the playbills and the number of playbills sold directly proportional? Justify your response. Assume the slope of the line was changed to -450. 10. Write the equation that could be used to represent this new relationship between the price of the playbills and the number of playbills sold. 11. Describe any changes in the graph that would result from this change in the slope. Number of T-shirt Sold The Band Boosters Club at Newland High School 1400is planning to sell t-shirts to raise money for new instruments. The shirts will be designed with the school colors and mascot on the front. The Boosters must consider how much to charge 1200for each t-shirt, and how much money can be raised 1000 The Band Booster Treasurer has researched previous years’ sales records and organized the results in the following table. Graph the data on the grid below. 800 Band Boosters T-Shirt Sales Number T-shirt of T-Shirts Price Sold $1.50 1350 $3.00 1200 $4.50 1050 $6.50 850 $9.00 600 600 400 0 200 2 4 2 6 8 2 2 T-shirt Price 10 2 12 2 12. Draw a line through the points on your graph. 13. The relationship between the price and the number of t-shirts sold is linear. Justify this statement using both the table and the graph. 14. Determine the slope of the line through the points. 15. Describe the meaning of the slope in this problem situation. 16. Use the data in the table and the graph to determine the y-intercept of the line through the data points. 17. Describe the meaning of the y-intercept in this problem situation. 18. Write the equation of the line through the data points in slope-intercept form. 19. Is the relationship between the price of the t-shirts and the number of t-shirts sold directly proportional? Justify your response. Assume the slope of the line was changed to -75. 20. Write the equation that could be used to represent this new relationship between the price of the t-shirts and the number of t-shirts sold. 21. Describe any changes in the graph that would result from this change in the slope. 480 Number of Ornament Sold 420 Each hospital has an auxiliary group, which is a volunteer group whose focus is to raise money 0 to help fund projects at the hospital. The auxiliary group at Mercy Hospital would like to sell 360 holiday ornaments to raise funds to help purchase The chairman of the finance committee has researched previous years’ sales records and 300 organized the results in the following table. Graph the data on the grid below. Mercy Hospital Auxiliary Holiday Ornament Sales Number of Ornament Ornaments Price Sold $3.50 345 $4.50 315 $6.00 270 $8.50 195 $10.00 150 240 180 120 60 2 4 2 6 8 2 2 Ornament Price 10 2 12 2 22. Draw a line through the points on your graph. 23. The relationship between the price and the number of ornaments sold is linear. Justify this statement using both the table and the graph. 24. Determine the slope of the line through the points. 25. Describe the meaning of the slope in this problem situation. 26. Use the data in the table and the graph to determine the y-intercept of the line through the data points. 28. Write the equation of the line through the data points in slope-intercept form. 27. Describe the meaning of the y-intercept in this problem situation. 29. Is the relationship between the price of the ornaments and the number of ornaments sold directly proportional? Justify your response. Assume the slope of the line was changed to -25. 30. Write the equation that could be used to represent this new relationship between the price of the ornaments and the number of ornaments sold. 31. Describe any changes in the graph that would result from this change in the slope.

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