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**Lesson 5: Graphing Stories**

Note Packet A Lesson 5: Graphing Stories

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**Lesson 5: Graphing Stories**

Exercise 1: Consider this story Maya and Earl live at opposite ends of the hallway in their apartment building. Their doors are 50 feet apart. They each start at their door and walk at a steady pace towards each other and stop when they meet What would their graphing stories look like if we put them on the same graph? When the two people meet in the hallway, what would be happening on the graph? Sketch a graph that shows their distance from Maya’s door.

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**Thoughts before we graph: x-axis = Time y-axis = distance 50 feet**

Maya and Earl live at opposite ends of the hallway in their apartment building. Their doors are 50 feet apart. They each start at their door and walk at a steady pace towards each other and stop when they meet Thoughts before we graph: x-axis = Time What should go on the x axis? y-axis = distance What should go on the y axis? 50 feet How far apart are they to start?

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Maya and Earl live at opposite ends of the hallway in their apartment building. Their doors are 50 feet apart. They each start at their door and walk at a steady pace towards each other and stop when they meet Thoughts before we graph: Earl x-axis = Time 50 y-axis = distance 40 50 feet Distance (ft) 30 Point of Intersection 20 10 Maya Time What would their graphing stories look like if we put them on the same graph? When the two people meet in the hallway, what would be happening on the graph? The two lines intersect

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**Exercise 2: Consider this story**

Duke starts at the base of a ramp and walks up it at a constant rate. His elevation increases by three feet every second. Just as Duke starts walking up the ramp, Shirley starts at the top of the same 25 foot high ramp and begins walking down the ramp at a constant rate. Her elevation decreases two feet every second Shirley 24 1. Sketch two graphs on the same set of elevation-versus-time axes to represent Duke’s and Shirley’s motions 22 20 18 16 14 Elevation (ft) 12 10 8 6 4 2 Duke 1 2 3 4 5 6 7 8 9 10 Time

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**Exercise 2: Consider this story**

Duke starts at the base of a ramp and walks up it at a constant rate. His elevation increases by three feet every second. Just as Duke starts walking up the ramp, Shirley starts at the top of the same 25 foot high ramp and begins walking down the ramp at a constant rate. Her elevation decreases two feet every second 2. What are the coordinates of the point of intersection of the two graphs? At what time do Duke and Shirley pass each other? Point of Intersection (5, 15) 5 Seconds

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**Exercise 2: Consider this story**

3. Duke’s motion can be modeled by the equation y = 3t and Shirley’s can be modeled by the equation y = 25 – 2t. Show that the coordinates of the point you found in the question above satisfy both equations Point of Intersection (5, 15) Duke y = 3t 15 = 3 (5) 15 = 15 Shirley y = 25 – 2t 15 = 25 – 2 (5) 15 = 25 – 10 15 = 15

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**Exercise 3: Watch the following video**

1. Graph the man's elevation on the stairway versus time in seconds 11 10 9 8 7 Elevation (ft) 6 5 4 3 2 1 Man 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 Time (sec)

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**Exercise 3: Watch the following video**

2. Add the girl’s elevation to the same graph. How did you account for the fact that the two people did not start at the same time? Started the man at 0 seconds Started the girl at 21 seconds 11 10 9 8 7 Elevation (ft) 6 5 4 3 2 1 Man 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 Time (sec) Girl

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**Exercise 3: Watch the following video**

3. Suppose the two graphs intersect at the point P(24,3). What is the meaning of this point in this situation? Point of Intersection. Where the people meet 11 10 9 8 7 Elevation (ft) 6 5 4 3 2 1 Man 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 Time (sec) Girl

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**Exercise 3: Watch the following video**

4. Is it possible for two people, walking in stairwells, to produce the same graphs you have been using and NOT pass each other at time 24 seconds? Explain your reasoning. Yes. They could be in 2 different stair wells 11 10 9 8 7 Elevation (ft) 6 5 4 3 2 1 Man 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 Time (sec) Girl

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**It represents the solution to both equations**

In Closing What is a point of intersection? What does it represent? Where the 2 lines cross It represents the solution to both equations

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