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Slope, Linear Whole Day Lesson

Author:Arpit Kesharwani, Steve Phelps, Tim Brzezinski
Lesson 4Problem 1A contractor must haul a large amount of dirt to a work site. She collected information from two hauling companies. EZ Excavation gives its prices in a table. Happy Hauling Service gives its prices in a graph. dirt (cubic yards)cost (dollars)row 1row 2row 3
  1. How much would each hauling company charge to haul 40 cubic yards of dirt? Explain or show your reasoning.  
  2. Calculate the rate of change for each relationship. What do they mean for each company?
  3. If the contractor has 40 cubic yards of dirt to haul and a budget of $1000, which hauling company should she hire? Explain or show your reasoning.  
Problem 2Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walk for a total of 5 hours. Who walks more steps? How many more?Problem 3 (from Unit 2, Lesson 11)Find the coordinates of point D in each diagram:Problem 4 (from Unit 2, Lesson 11)Select all the pairs of points so that the line between those points has slope 23.
  1. (0,0) and (2,3)
  2. (0,0) and (3,2)
  3. (1,5) and (4,7)
  4. (-2,-2) and (4,2)
  5. (20,30) and (-20,-30)
Lesson 5Problem 1A restaurant offers delivery for their pizzas. The total cost is a delivery fee added to the price of the pizzas. One customer pays $25 to have 2 pizzas delivered. Another customer pays $58 for 5 pizzas. How many pizzas are delivered to a customer who pays $80?Problem 2To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor.
  1. How much would the painting company charge to paint a house that needs 20 hours of labor? A house that needs 50 hours?
  2. Draw a line representing the relationship between x, the number of hours it takes the painting company to finish the house, and y, the total cost of painting the house. Label the two points from the earlier question on your graph.
  3. Find the slope of the line. What is the meaning of the slope in this context?
Problem 3 (from Unit 3, Lesson 4)Tyler and Elena are on the cross country team.Tyler's distances and times for a training run are shown on the graph.Elena’s distances and times for a training run are given by the equation y=8.5x, where x represents distance in miles and yrepresents time in minutes.
  1. Who ran farther in 10 minutes? How much farther? Explain how you know.
  2. Calculate each runner's pace in minutes per mile.
  3. Who ran faster during the training run? Explain or show your reasoning.
Problem 4 (from Unit 2, Lesson 12)Write an equation for the line that passes through (2,5) and (6,7).

Review

Assesment/Exit Ticket

  1. For each graph, record:vertical changehorizontal changeslope
  2. Describe a procedure for finding the slope between any two points on a line.
  3. Write an expression for the slope of the line in the graph using the letters u,v,s,u,v,s, and tt.

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