PowerPoint Presentation

Unit 4 Lesson 7Demonstrating Mastery

Unit 4 Lesson 7

1M.8.SP.3To 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.

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.2Performance Task for Demonstration of MasteryTask: 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?

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?3Worlds Fastest Roller Coasters

Pay attention to the values on the x and y axis. Study the informally fitted line. Locate points along the line where it crosses the grid lines. 4Task AnswersFind the equation of the lineFirst calculate the slope. Use points (350,100) and (450,120). m= 120-100 = 20 = 0.2 450-350 100Next, determine the y-intercept.y = mx+b100 = 0.2(350) + b30 = b Therefore, the equation of the line is y = 0.2x + 30

Select points (350,100) and (450,120) to calculate the slope of the line. These points are at the intersection of the grid lines in the graph, so it is easy to determine the coordinates of these points.

5Task AnswersUse 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 mphThe observed speed is 7 mph faster than the predicted speed.

Use the scatter plot to determine the observed value of the height and speed of the fastest roller coaster.6Task AnswersWhat 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 feety = 0.2x + 30y = 0.2(470) + 30y = 124The predicted top speed for a roller coaster that has a maximum height of 470 feet would be 124 mph. Max height of 350 feety = 0.2x + 30y = 0.2(350) + 30y = 100The predicted top speed for a roller coaster that has a maximum height of 350 feet would be 100 mph.

Substitute the x with 470 to calculate the top speed for a roller coaster with a maximum height of 470 feet. Then replace the x with 350 to calculate the top speed for a roller coaster with a maximum height of 350 ft.7Task AnswersWhat 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.

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.

8