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.