What is being compared to find the slope ratio? What would it look like in another representation? CPM Materials modified by Mr.

Transcription

1 Common Core Standard: 8.EE.5 8.EE.6 What is being compared to find the slope ratio? What would it look like in another representation? CPM Materials modified by Mr. Deyo

2 Title: IM8 Ch Can I Connect Rates To Slopes? Date: Learning Target By the end of the period, I will write equations representing proportional relationships and connect the constant of proportionality to the slope of a graph to the unit rate. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity.

3 Home Work: Sec Desc. Date Due Review & Preview 3 Problems: 7 81, 7 85, 7 86

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5 1) Slope Vocabulary 2) Positive Slope 3) Negative Slope 4) Proportion

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7 7.2.5 Can I Connect Rates To Slopes? In Chapter 1, you identified proportional relationships in both tables and graphs. Today you will look at the connection between slope and graphs of a proportional relationship. As you work with your study team today, keep the following questions in mind: What is being compared to find the slope ratio? What would it look like in another representation?

8 7 77a,b,c. POLITICAL POLL Mr. Mears was running for mayor of Atlanta. His campaign managers were eager to determine how many citizens of Atlanta would vote for him in the upcoming election. They decided to pay a respected, impartial statistical company to survey potential voters (a process called polling ) to find out how many people would probably vote for Mr. Mears. One afternoon, pollsters called 100 random potential voters in Atlanta to ask them how they would vote in the election. During that survey, 68 people indicated that they would vote for Mr. Mears. a) If the pollsters had instead called 50 randomly selected potential voters, predict how many of them would have said that they would vote for Mr. Mears. b) Do you suppose that this relationship is proportional? Why or why not? c) Carina s neighborhood has 327 potential voters. If voting in her neighborhood is similar to that of the poll, how many neighbors will probably vote for Mr. Mears? Complete the table at right.

9 7 77(continued) d) Make a graph of the data Carina has collected, and draw a line through the points. Should your line go through the origin? How do you know? e) What is the equation of the line in y = mx + b form? y = ( )x + ( ) f) Use the equation to help Carina figure out how many people will probably vote for Mr. Mears if 350,125 people vote in the election. g) What information would the unit rate give Carina? What is the unit rate? How does the unit rate compare to the slope? What do x and y represent in your equation?

10 7 78a,b. In two minutes, Stacie can write her name 17 times. a) Use a proportion (write equivalent ratios) to find how long it will take Stacie to write her name 85 times. b) Make a graph of this situation. Which piece of information is on the dependent axis?

11 7 78(continued). In two minutes, Stacie can write her name 17 times. c) Another name for the slope in a proportional relationship is the constant of proportionality. Find the constant of proportionality and write an equation in y = mx + b form for Stacie s situation. What do x and y represent in this situation? y = ( )x + ( ) d) Use the equation to find how many minutes it will take Stacie to write her name 85 times. e) What is the advantage of the equation in part (d) compared to the proportion (equivalent ratios) in part (a)? What is the advantage of the proportion? f) What is the unit rate at which Stacie writes her name?

12 7 79. Beth and her father have a large model railroad in their basement. Beth figured 260 x relates the length of an item on her model railroad 3 out that the equation y = to the length of the real thing, where x is the size on the model and y is the real object s size. Beth s uncle has a different model railroad in his home. It has a different scale. He put together the following table for Beth. a) In decimal notation, what is the unit rate for Beth s railroad? For her uncle s railroad? Make sure you show units on your unit rate. Beth s railroad b) On which model would a horse be taller? Use the unit rates to justify your answer without making any calculations.. Uncle s railroad.

13 7 80. Eight of 29 students in your class want to attend the Winter Ball. a) Find the constant of proportionality, b) If your class represents the entire school, how many of the 1490 students will probably attend the dance? (Use your constant of proportionality to set up a proportion. Then, solve your proportion.) and then write an equation in y = mx + b form. y = ( )x + ( ) What do x and y represent?

14 7 81. Aja and Emilie were riding their skateboards. They knew that they could ride 3 miles in 20 minutes. chapter/ch7/lesson a) How far can the girls ride in 45 minutes? b) If y represents the distance in miles and x represents the time in minutes, write an equation to represent the distance traveled for any time.

15 7 82. Joe is downloading songs from the Internet. He can download them at a rate of 8 songs every 10 minutes. Jasmine, who is also downloading songs, can download at a rate of 12 songs every 15 minutes. homework/homework/categ chapter/ch7/lesson/7.2.5/problem/7 82 Who is downloading songs faster? is downloading songs faster.

16 7 83. Reflect quadrilateral ABCD across the line y = 2. Write the new coordinate points. chapter/ch7/le Graph A (, ) B (, ) 5 A B y D C 5 x A' (, ) B' (, ) C (, ) D (, ) 5 C' (, ) D' (, )

17 7 84 Complete each of the Diamond Problems below. The pattern used in the Diamond Problems is shown at right. homework/homework/category/cc/textbook/cc3/ chapter/ch7/lesson/7.2.5/problem/7 84

18 7 85. Graph the line that goes through the points ( 6, 3) and ( 3, 1). chapter/ch7/ Graph a) What is the slope of the line? b) Where's the y intercept? (, ) c) Find the equation of the line. y = ( )x + ( )

19 7 86. Mr. Crow, the head groundskeeper at High Tech Middle School, mows the lawn along the side of the gym. The lawn is rectangular, and the length is 5 feet more than twice the width. The perimeter of the lawn is 250 feet. a) Define a variable and write an equation for this problem. chapter/ch b) Solve the equation that you wrote in part (a) and find the dimensions of the lawn. c) Use the dimensions you calculated in part (a) to find the area of the lawn.