Relationships In Data. Lesson 10

Transcription

1 Relationships In Data Lesson 0

2 Lesson Ten Concepts Overall Epectations Appl data-management techniques to investigate relationships between two variables; Determine the characteristics of linear relations; Demonstrate an understanding of the constant rate of change and its connection to linear relations; Connect various representations of a linear relation, and solve problems using the representations. Specific Epectations Interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant; Pose problems, identif variables, and formulate hpotheses associated with relationships between two variables; Describe trends and relationships observed in data, make inferences from data, compare the inferences with hpotheses about the data, and eplain an differences between the inferences and the hpotheses; Construct tables of values and graphs, using a variet of tools; Construct tables of values, scatter plots, and lines or curves of best fit as appropriate using a variet of tools; Determine values of a linear relation b using a table of values, b using the equation of the relation, and b interpolating or etrapolating from the graph of the relation. Relationships in Data Tables and graphs of data help to show the relationships between quantities. In mathematics the relationship between a pair of quantities is called a relation. Eample Use the graph following to answer each question. a) State the percentage of Canadians who enjo professional wrestling for each of the following ears. Show the popularit in a table b) When did the popularit of professional wrestling reach 6% of all Canadians? Copright 005, Durham Continuing Education Page 9 of 5

3 Solution a) State the percentage of Canadians who enjo professional wrestling for each of the following ears? Show the popularit in a table Year Popularit (%) b) When did the popularit of professional wrestling reach 6% of Canadians? Approimatel 985 Copright 005, Durham Continuing Education Page 30 of 5

4 Eample Which graph below best represents each situation? a) the height of a person over time b) the height of roller coaster over time c) the amount of hours of sunlight over a ear d) the number of D.V.D. plaers sold compared to selling price Solution i) ii) iii) iv) Which graph below best represents each situation? a) the height of a person over time b) the height of roller coaster over time c) the amount of hours of sunlight over a ear d) the number of D.V.D. plaers sold compared to selling price i) ii) iii) iv) a d c b Support Questions. Use the graph following to answer each question. a) What ear was Canada s population in the following ears? b) When did Canada s population reach 5 million? Copright 005, Durham Continuing Education Page 3 of 5

5 Canadians Population Since Population (millions) Year. Brianna walks to her grandparents. This graph shows her distance from home during one of her walks. Describe her walk. 3. Noah is riding his bike from his grandparents to his home. Describe Noah s possible ride home Copright 005, Durham Continuing Education Page 3 of 5

6 Support Questions 4. Refer to the graph given below: a) How man tetbooks make the following heights? 45 cm, 60cm, 75cm b) Approimatel how high is the following number of tetbooks? 7 books, 9 books, 4 books, books 5. a) Construct a graph using this data. Number of stairs climbed Height (cm) b) Did ou join the points? Eplain. c) What is the height of 5 stairs? d) How man stair will reach a height of 444 cm.? e) If the number of stairs is doubled will the height double? Eplain. Copright 005, Durham Continuing Education Page 33 of 5

7 Support Questions 6. a) Construct a graph using this data. Radius of a circle, (cm) Area of a circle. ( cm ) b) Did ou join the points? Eplain. c) What is the approimate radius of circle with an area of 00cm? d) What is the approimate area of circle with a radius of 4.5 cm? e) If the radius is doubled will the area double? Eplain. Graphing Relations Relations can be either linear or non-linear. Linear means the relation forms a single straight line and non-linear produces anthing that is not a single straight line. The following formula is used: slope = z Eample Draw a graph of the relation described b the equation. a) = 3 + Copright 005, Durham Continuing Education Page 34 of 5

8 Solution a) = 3 + First step is to make a table of values and choose values to place in column of table Second step is to substitute each value into the equation to determine the value. For = - = 3+ = 3(-)+ = 6 + = For = - = 3+ = 3(-)+ = 3 + = For = 0 Copright 005, Durham Continuing Education Page 35 of 5

9 = 3+ = 3(0)+ = 0 + = For = = 3+ = 3()+ = -3 + = For = = 3+ = 3()+ = -6 + = Net, plot the coordinates (, ) on a grid and join the points with a straight edge and label the equation. Copright 005, Durham Continuing Education Page 36 of 5

10 Support Questions 7. Complete the table of values. a) = 5 b) = + 6 c) = The cost of D dollars, to print and bind copies of a earbook is given b the equation D = 60 +0n. a) Make a table of values to show the costs for up to 400 Yearbooks. b) Use the table to draw a graph. c) Use the graph to estimate the cost of 35 copies. d) Use the graph to estimate how man copies can be made for $50. Copright 005, Durham Continuing Education Page 37 of 5

11 Support Questions 9. Complete a table of values and graph each relation. a) = 3 4 b) = + c) C = 5. 5 w Which of the following ordered pairs satisf the relation modelled b = Show b substituting the values into the relation. a) (-3, 6) b) (4, 5) c) (7, 3.5) d) (-4, 9) e) (-4, 6.5) Ke Question #0. Which graph below best represents each situation? (4 marks) a) the height of a person over time b) the height of roller coaster over time c) the amount of hours of sunlight over a ear d) the number of D.V.D. plaers sold compared to selling price i) ii) iii) iv). Complete a table of values and graph each relation. (8 marks) a) C = 3n + 0 b) = 4 c) W = 4.75n. 50 d) P = l The time that passes between the time ou see lightning and ou hear the thunder depends on our distance from the lightning. With each km from the lightning 3 seconds pass. (4 marks) a) Make a table of values for distances from 0 to 5 km. b) Graph this relation. State whether it is a linear or non-linear relation. c) Using our graphed relation, how much time passes before ou hear lightning that occurs 4.5 km awa? d) Using our graphed relation, how far awa are ou if ou hear the thunder in.5 seconds? Copright 005, Durham Continuing Education Page 38 of 5

12 Ke Question #0 (continued) 4. The amount a tai driver charges a customer is given b the equation A =.5k + 5.5, where A is the total amount charged and k is the kilometres driven. (5 marks) a) What do the numbers in the equation represent? b) Make a table of values for distances from 0 to 0 km. c) Graph this relation. State whether it is a linear or non-linear relation. d) Using our graphed relation, how much is charged if a person goes 7.5 km? e) Using our graphed relation, how far can a person go in a tai for $5? 5. Ashlee repairs DVD plaers. She charges $5 to inspect the problem and $0/h to repair the device. (5 marks) a) Write an equation to model this relation. b) Make a table of values. c) Graph this relation. d) Using our graphed relation, how long did it take Ashlee to repair the DVD plaer if she charged $55? e) Using our graphed relation, how much should Ashlee charge if it takes her 4.5 hours to repair the DVD plaer? Copright 005, Durham Continuing Education Page 39 of 5