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Unit 4 Lesson 7 Demonstrating Mastery M.8.SP.3 To demonstrate mastery of the objectives in this lesson you must be able to:  Interpret the slope and.

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Presentation on theme: "Unit 4 Lesson 7 Demonstrating Mastery M.8.SP.3 To demonstrate mastery of the objectives in this lesson you must be able to:  Interpret the slope and."— Presentation transcript:

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2 Unit 4 Lesson 7 Demonstrating Mastery

3 M.8.SP.3 To demonstrate mastery of the objectives in this lesson you must be able to:  Interpret the slope and intercept of an line that has been informally fitted to a linear trend in a scatter plot.  Use the slope and intercept to write an equation for the linear model.  Use the equation of the linear model to solve problems in context of bivariate measurement data. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

4 Performance Task for Demonstration of Mastery Task: The scatter plot on the next slide shows the height and speed of some of the tallest and fastest roller coasters in the world. A line has been informally fitted to the data trend.  Find the equation of the line. Show your steps.  Use the equation to find the difference (observed value – predicted value) for the fastest roller coaster.  What would be the top speed of a roller coaster with a maximum height of 470 feet? 350 feet?  What does the slope of the line indicate between the height and speed of the roller coaster?

5 World’s Fastest Roller Coasters

6 Task Answers Find the equation of the line First calculate the slope. Use points (350,100) and (450,120). m= 120-100 = 20 = 0.2 450-350 100 Next, determine the y-intercept. y = mx+b 100 = 0.2(350) + b 30 = b Therefore, the equation of the line is y = 0.2x + 30

7 Task Answers Use the equation to find the difference (observed value – predicted value) for the fastest roller coaster. The Fastest Roller Coaster has an observed height of approximately 455 feet and speed of 128 mph. However, using the equation y = 0.2x + 30, the predicted speed would be y = 0.2(455) + 30 y = 121 mph The observed speed is 7 mph faster than the predicted speed.

8 Task Answers What should you predict the top speed of a roller coaster with a maximum height of 470 feet to be? 350 feet? Max height of 470 feet y = 0.2x + 30 y = 0.2(470) + 30 y = 124 The predicted top speed for a roller coaster that has a maximum height of 470 feet would be 124 mph. Max height of 350 feet y = 0.2x + 30 y = 0.2(350) + 30 y = 100 The predicted top speed for a roller coaster that has a maximum height of 350 feet would be 100 mph.

9 Task Answers What does the slope of the line indicate between the height and speed of the roller coaster? The slope indicates that the speed increases 0.2 mph for every 1 foot of track height. This means that the speed of the roller coaster increases 20 mph for every 100 feet of track height.


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