Julie is planning a party and comparing the cost at different banquet halls. At Parties R...

  

Transcribed Image Text:

Julie is planning a party and comparing the cost at different banquet halls. At Parties R Us, the charge is $20 per person. At Elegant Banquets, the charge is $15 per person. Complete the tables to show the total cost for different numbers of people. Parties R Us Elegant Banquets Number of People (hours) 0 25 50 75 100 Total Cost (dollars) Number of People 0 25 50 75 100 Total Cost (dollars) Write an equation to represent the cost at each banquet hall, where x represents the number of people and y represents the total cost. Total Cost (dollars) Lines y, and y, represent the cost at each banquet hall. Determine which line represents each banquet hall. Explain your reasoning. YA 1800- 1600- y -Y2 1400- 1200 1000- 800 600 400- 200 0 20 40 60 80 100 120 140 160180 Number of People X Describe the similarities and differences in each of the graphs, tables, and equations that represent the proportional relationships. 2 Casey and Allison are making bracelets to sell at a street fair. The number of bracelets they have completed at the end of each week are shown below. Casey Allison Time Worked Total Bracelets (weeks) Made Time Worked (weeks) Total Bracelets Made 5 150 3 160 6 180 7 360 8 240 10 510 9 270 12 610 Determine the rate at which each person works. Show your work. 3 Consider the graph. YA Gasoline Remaining (gallons) 18 16 14 12 10 8 9 4 2- 0 40 80 120 160 200 240 280 320 360 Distance Traveled (miles) X a Determine the rate of change shown in the graph.srt ins Restate the rate of change as a unit rate. Explain its meaning. Is the relationship shown in the graph proportional? Explain your reasoning. Did either girl already have bracelets made ready to sell? Show your work and explain your reasoning. Write an equation to represent the number of bracelets each girl makes. Are the relationships proportional? Explain your reasoning. Michele is also making bracelets for the street fair and has no bracelets ready to sell. At the end of 15 weeks, she has 450 bracelets made. Does Michele make bracelets at the same rate as Casey or Allison? Explain your reasoning. 3 Consider the graph. YA 18 16 14 12 Gasoline Remaining (gallons) 10 00 64 2 0 40 80 120 160 200 240 280 320 360 Distance Traveled (miles) X Determine the rate of change shown in the graph. b Restate the rate of change as a unit rate. Explain its meaning. Is the relationship shown in the graph proportional? Explain your reasoning. 4 Consider the following table. Is the relationship proportional? Explain your answer. y X -8 -1 -2 3.5 10 12.5 20 20 5 Jose is making mango smoothies. Jose used three 16-ounce containers of plain yogurt. He made 15 servings of smoothies. @ What is the rate of the number of ounces of yogurt per smoothie? How much of a smoothie can Jose make with 1 ounce of plain yogurt? Jose reasons that if he doubles the number of 16-ounce containers of plain yogurt, he can make 30 servings of smoothies. Is Jose correct? Justify your response. 6 What is the slope of a line through the points A (2, 17) and B (-5, -11)? 7 Consider the points A (2,-5) and B (0, 6). Plot the points to determine the slope of line AB. 8+ 4+ 2+ 0 -8-6-4 4 6 8 -2- -4+ -6+ -8+ AX 8 Consider each of the following relationships. In school A, the ratio of male students to female students is 5:2. In school B, the relationship between the number of male students, y, and the number of female students, x, is given by the equation y = x. . In school C, the number of male and female students are as shown in the table. Female Students 120 Male Students 200 Which school shows the greatest rate of change between male and female students? Explain your reasoning. 9 Consider the graph. YA 8 6 4+ 2-A B C 2 4 6 8 -8-6-4 -2 -4 214 -6+ -8. DO AX Create a right triangle using points A and B. Label the triangle with horizontal and vertical distances, then determine the rate of change between the pair of points. Create a right triangle using points C and D. Label the triangle with horizontal and vertical distances, then determine the rate of change between the pair of points. Determine the slope of the line. @ Write an equation for the line. 10 Kevin has been knitting a large blanket and spent 3 hours working on it today. After 1 hour of work today, he had 32 rows completed. After 3 hours of work today, he had 40 rows completed. Let y be the number of rows completed after x hours of knitting. Identify and interpret the slope for this situation. Julie is planning a party and comparing the cost at different banquet halls. At Parties R Us, the charge is $20 per person. At Elegant Banquets, the charge is $15 per person. Complete the tables to show the total cost for different numbers of people. Parties R Us Elegant Banquets Number of People (hours) 0 25 50 75 100 Total Cost (dollars) Number of People 0 25 50 75 100 Total Cost (dollars) Write an equation to represent the cost at each banquet hall, where x represents the number of people and y represents the total cost. Total Cost (dollars) Lines y, and y, represent the cost at each banquet hall. Determine which line represents each banquet hall. Explain your reasoning. YA 1800- 1600- y -Y2 1400- 1200 1000- 800 600 400- 200 0 20 40 60 80 100 120 140 160180 Number of People X Describe the similarities and differences in each of the graphs, tables, and equations that represent the proportional relationships. 2 Casey and Allison are making bracelets to sell at a street fair. The number of bracelets they have completed at the end of each week are shown below. Casey Allison Time Worked Total Bracelets (weeks) Made Time Worked (weeks) Total Bracelets Made 5 150 3 160 6 180 7 360 8 240 10 510 9 270 12 610 Determine the rate at which each person works. Show your work. 3 Consider the graph. YA Gasoline Remaining (gallons) 18 16 14 12 10 8 9 4 2- 0 40 80 120 160 200 240 280 320 360 Distance Traveled (miles) X a Determine the rate of change shown in the graph.srt ins Restate the rate of change as a unit rate. Explain its meaning. Is the relationship shown in the graph proportional? Explain your reasoning. Did either girl already have bracelets made ready to sell? Show your work and explain your reasoning. Write an equation to represent the number of bracelets each girl makes. Are the relationships proportional? Explain your reasoning. Michele is also making bracelets for the street fair and has no bracelets ready to sell. At the end of 15 weeks, she has 450 bracelets made. Does Michele make bracelets at the same rate as Casey or Allison? Explain your reasoning. 3 Consider the graph. YA 18 16 14 12 Gasoline Remaining (gallons) 10 00 64 2 0 40 80 120 160 200 240 280 320 360 Distance Traveled (miles) X Determine the rate of change shown in the graph. b Restate the rate of change as a unit rate. Explain its meaning. Is the relationship shown in the graph proportional? Explain your reasoning. 4 Consider the following table. Is the relationship proportional? Explain your answer. y X -8 -1 -2 3.5 10 12.5 20 20 5 Jose is making mango smoothies. Jose used three 16-ounce containers of plain yogurt. He made 15 servings of smoothies. @ What is the rate of the number of ounces of yogurt per smoothie? How much of a smoothie can Jose make with 1 ounce of plain yogurt? Jose reasons that if he doubles the number of 16-ounce containers of plain yogurt, he can make 30 servings of smoothies. Is Jose correct? Justify your response. 6 What is the slope of a line through the points A (2, 17) and B (-5, -11)? 7 Consider the points A (2,-5) and B (0, 6). Plot the points to determine the slope of line AB. 8+ 4+ 2+ 0 -8-6-4 4 6 8 -2- -4+ -6+ -8+ AX 8 Consider each of the following relationships. In school A, the ratio of male students to female students is 5:2. In school B, the relationship between the number of male students, y, and the number of female students, x, is given by the equation y = x. . In school C, the number of male and female students are as shown in the table. Female Students 120 Male Students 200 Which school shows the greatest rate of change between male and female students? Explain your reasoning. 9 Consider the graph. YA 8 6 4+ 2-A B C 2 4 6 8 -8-6-4 -2 -4 214 -6+ -8. DO AX Create a right triangle using points A and B. Label the triangle with horizontal and vertical distances, then determine the rate of change between the pair of points. Create a right triangle using points C and D. Label the triangle with horizontal and vertical distances, then determine the rate of change between the pair of points. Determine the slope of the line. @ Write an equation for the line. 10 Kevin has been knitting a large blanket and spent 3 hours working on it today. After 1 hour of work today, he had 32 rows completed. After 3 hours of work today, he had 40 rows completed. Let y be the number of rows completed after x hours of knitting. Identify and interpret the slope for this situation.