Algebra. Chapter 5: LINEAR FUNCTIONS. Name: Teacher: Pd:

Transcription

1 Algebra Chapter 5: LINEAR FUNCTIONS Name: Teacher: Pd:

2 Day 1 - Chapter 5-3/5-4: Slope SWBAT: Calculate the slope from any two points Pgs. #1-5 Hw pgs. #6 7 Table of Contents Day 2 - Chapter 5-6: Slope Intercept Form SWBAT: Write and Graph a linear equation in Slope Intercept Form Pgs. #8 11 Hw pgs. #12 14 Day 3 - Chapter 5-7: Point - Slope Form SWBAT: Write and Graph a linear equation in Point - Slope Form Pgs. #15 19 Hw pgs. #20 21 Day 4 - Chapter 5-6/5-7: Vertical and Horizontal Lines SWBAT: Write and Graph Vertical and Horizontal Lines Pgs. #22-25 Hw pgs. #26-27 Day 5 - Review: Sections 5-2 through 5-7 Pgs. #28-31 Day 6 - Chapter 5-8: Slopes of Parallel and Perpendicular Lines SWBAT: Calculate the slope of Parallel and Perpendicular Lines Pgs. #32-37 Hw pgs. #38-39 Day 7 - Chapter 5-8: Equations of Parallel and Perpendicular Lines SWBAT: Write the equation of Parallel and Perpendicular Lines Pgs. #40-43 Hw pgs. #44-45 Day 8 - Chapter 5-5: Direct Variation SWBAT: Identify, write, and graph direct variations Pgs. #46-50 Hw pgs. #50-51 Day 9 10: Review of Chapter 5 SWBAT: Graph and Write Linear Equations Pgs. #52-66

3 Day 1 Slope Warm - Up Find the x- and y- intercepts. a. b. x-intercept: y-intercept: x-intercept: y-intercept: Motivation: The slope of a line measures the steepness of the line. We re familiar with the word slope as it relates to mountains. Skiers and snowboarders refer to hitting the slopes. Slope measures the ratio of the change in the y-value of a line to a given change in its x-value. Finding Slope DEFINITION OF SLOPE 1

4 Example 1: Calculating the slope from a Graph a: Find the slope of the line. b: Find the slope of the line. y y x x 1 st Point: 2 nd Point: 1 st Point: 2 nd Point: slope y x Y X Y X m slope m 2 1 y x Y X Y X 2 1 c: Find the slope of the line. d: Find the slope of the line. y y x x 1 st Point: 2 nd Point: 1 st Point: 2 nd Point: slope y x Y X Y X m slope m 2 1 y x Y X Y X 2 1 2

5 e. f. Example 2: Calculating the slope from a set up points a) Find the slope of the line that passes through the points 8, 7 and 4, 5. and Y m X Y X

6 b) Find the slope of the line that passes through the points (4, 3) and ( 5, 2). and Y m X Y X c) Find the slope of the line that passes through the points ( 4, 7) and ( 3, 5). and Y m X Y X Example 3: Calculating the Slope from a Table of Values a) Find the slope of the line that contains the points from the table b) Find the slope of the line that contains the points from the table 4

7 Challenge Summary Exit Ticket 1. Fill in the blanks. 2. 5

8 Day 1 Homework Slope 1) Find the slope of the line that passes through each of the following sets of points. (a) (b) (c) (d) (e) (f) 2) Find the slope of each of the following lines graphically: a) fkdjflkdjfjkd b) 6

9 c) d) 7

10 Day 2 - Slope Intercept Form Warm Up Motivation: Who uses this? 8

11 Graphing by using slope and y-intercept 1. 3 y x 2 m = 2. y 2x 4 m = 4 y-intercept = b = (0, ) y-intercept = b = (0, ) Practice Graphing by using slope and y-intercept 3. 1 y x 3 m = 4. y 3x m = 2 y-intercept = b = (0, ) y-intercept = b = (0, ) 9

12 5. Writing Equations of Graphs Write the equation in slope intercept form. Then graph the line described by the equation. 3x + 2y = 5 10

13 10. Write the equation in slope intercept form. Then graph the line described by the equation. 4x - 2y = 14 Challenge SUMMARY Exit Ticket 11

14 Day 2 Homework Slope Intercept Form 1) Which of the following lines has a slope of 5 and a y-intercept of 3? (1) y 5x 3 (3) y 3x 5 5 (2) y x 3 (4) y 3x 5 2) Which of the following equations represents the graph shown? y (1) 3 y x 3 (3) 2 2 y x 3 3 (2) 3 y x 2 (4) 2 2 y x 2 3 x 3) Graph each line. (a) y = 3x+ 2 (b) y = 1 x 2 12

15 (c) y = 6x + 3 (d) y = 2 3 x + 9 (e) y = x + 2 (f) y = x - 3 (g) y = - x - 4 (h) y = 2x

16 1) Write an equation of each line in slope intercept form. Identify the slope and y-intercept. a. 2x 2y 4 b. 5x y 7 c. 6x + 2y = 8 d. 10 5y 15 14

17 Day 3 Point Slope Form Warm Up 15

18 Yesterday, we learned how to graph equations using the slope and the y-intercept. Today we are going to write equations of lines. First, let s see how to use the equation. Example 1: Graph the linear equation. y 1 = 2(x 3) m = pt = (, ) Practice: Graph the linear equation. y + 4 = -¼(x 8) m = pt = (, ) Equations of Lines 16

19 Example 2: Converting Point-Slope to Slope-Intercept Form and Standard Form. Write in Slope-Intercept form and Standard Form. Practice: Converting Point-Slope form to Slope intercept Form Writing Equations of Lines Example 3: Write the equation of a line given the slope and a point. (-3, -4); m = 3 17

20 Practice: Write the equation of a line given the slope and a point. (1, 2); m = 3 Example 4: Write the equation of a line passing through the two points given. (10, 20) and (20, 65) Step 1: Step 2: plug m, and point into equation. y y 1 = m(x x 1 ) Practice: Write the equation of a line passing through the two points given. (2, 5) and ( 8, 5) Step 1: Step 2: plug m, and point into equation. y y 1 = m(x x 1 ) 18

21 Challenge Write the equation of a line in point-slope form passing through the two points given. (f, g) (h, j) SUMMARY Exit Ticket 19

22 Day 3 Point Slope Form - HW 1) Which equation describes the line through ( 5, 1) with the slope of 1? (a) y = x 6 (c) y = 5x + 6 (b) y = 5x 6 (d) y = x + 6 2) A line contains (4, 4) and (5, 2). What is the slope and y intercept? (a) slope = 2; y intercept = 2 (c) slope = 2; y intercept = 12 (b) slope = 1.2; y intercept = 2 (d) slope = 12; y intercept = 1.2 Write an equation for the line with the given slope and point in slope-intercept form. 3) slope = 3; ( 4, 2) 4) slope = 1; (6, 1 ) Equation: 5) slope = 0; (1, 8) Equation: 6) slope = 9; ( 2, 3) Equation: Equation: 20

23 Write an equation for the line through the two points in slope intercept form. 7) (2, 1); (0, 7) 8) ( 6, 6); (2, 2) Equation: 9) ( 2, 3); ( 1, 4) Equation: 10) (6, 12); (0, 0) Equation: Equation: Write an equation for the line for each graph. 11) 12) 21

24 Day 4 Vertical and Horizontal Lines Warm Up: Horizontal Lines Picture: Slope = If your point is (a, b), then your equation is always y = Ex: Write the equation of the horizontal line passing through each point. 1. (3, 7) 2. (2, -4) 3. (8, 0)

25 Vertical Lines Picture: Slope = If your point is (a, b), then your equation is always x = Ex: Write the equation of the vertical line passing through each point. 7. (2, 9) 8. (1, -3) 9. (0, 10) Parallel Lines Parallel Lines have the slope What can you say about all horizontal lines? 23

26 What can you say about all vertical lines? What can you say about a horizontal line and a vertical line? Write the equation of the line Parallel to y = 4, through (2, -3) 14. Parallel to x = -3, through (1, 2) 15. Parallel to the y-axis through (2, 4) 16. Parallel to the x-axis through (3, -5) 17. Through (2, 8) with a slope of Through (3, 3) with an undefined slope. 24

27 Write the slope-intercept form of the equation of the line through the given points. 1) through: (5, -2) and (0, -2) 8) through: (-6, -1) and (-6, 11) Challenge Write the equation of a line perpendicular to y = 1, passing through (2, 10). SUMMARY Memory Device for Vertical Lines Memory Device for Horizontal Lines x = a value of point = (a, b) y = b value of point = (a, b) 1. Exit Ticket 2. 25

28 Day 4 - HW 26

29 13) Write the equation of a line parallel to x = 12 passing through the point (4, 5). 14) Write the equation of a line parallel to y = 1 passing through the point (-3, 7). 15) Write the equation of a line parallel to the x-axis passing through the point (1, 1). 16) Write the equation of a line parallel to the y-axis passing through the point (-8, 0). 27

30 Day 5 Review of Sections 5-2 through

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33 Write the equation of the lines below. Write your answer in slope-intercept form. 31

34 Day 6 Slopes of Parallel and Perpendicular Lines Warm Up Directions: Find the reciprocal. 1) 2 2) 3 1 Directions: Find the slope of the line that passes through each pair of points. 4) (2, 2) and ( 1, 3) 5) (3, 4) and (4, 6) 6) (5, 1) and (0, 0) 3)

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37 Example 3: Graph a line parallel to the given line and passing through the given point. Graph a line perpendicular to the given line and passing through the given point. 35

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39 Challenge x 1 If PQ RS and the slope of PQ and the slope of RS is 6, then find the value of x. Justify 4 8 algebraically or numerically. SUMMARY Exit Ticket

40 Day 6 Slopes of Parallel and Perpendicular Lines HW 38

41 7) 8) 9) 10) 39

42 Day 7 Equations of Parallel and Perpendicular Lines Warm Up Determine the equation of the line that passes through the two points 4, 2 and, ) Write an equation for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8. Step 1: m = Step 2: plug in the point into y y 1 = m(x x 1 ) and solve for y. Equation: 2) Write an equation for the line that passes through ( 2, 5) and is parallel to the line described by y = 2 1 x 7. Step 1: m = Step 2: plug in the point into y y 1 = m(x x 1 ) and solve for y. Equation: 40

43 3) Write an equation for the line that passes through (2, 1) and is perpendicular to the line described by y = 2x 5. Step 1: m = Step 2: plug in the point into y y 1 = m(x x 1 ) and solve for y. Equation: 4) Write an equation for the line that passes through (2, 6) and is perpendicular to the line described by y = x + 2. Step 1: m = Step 2: plug in the point into y y 1 = m(x x 1 ) and solve for y. Equation: 41

44 Regents Practice 5) What is the slope of a line parallel to the line whose equation is y = -4x + 5? 6) What is the slope of a line parallel to the line whose equation is 3x + 6y = 6? 7) 8) Kjk 42

45 Challenge SUMMARY Exit Ticket

46 Day 7 Equations of Parallel and Perpendicular Lines - HW 44

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48 Day 8 Direct Variation Warm Up Find the slope of the linear function represented by the table below. 1) 2) Motivation: Who uses this? A recipe for paella calls for 1 cup of rice to make 5 servings. In other words, a chef needs 1 cup of rice for every 5 servings. The equation y = 5x describes this relationship. In this relationship, the number of servings varies directly with the number of cups of rice. 46

49 Direct Variation Example1: Identifying Direct Variations from an Equation Tell whether the equation represents a direct variation. If so, identify the constant of variation. 1) y = 21x 2) 3x + y = 8 Direct Variation? Constant of Variation: Direct Variation? Constant of Variation: 3) 4x + 3y = 0 4) 3x + 0 = 15y Direct Variation? Constant of Variation: Direct Variation? Constant of Variation: What happens if you solve y = kx for k? Let s see In a direct variation, the ratio is equal to the constant of variation. 47

50 Example 2: Identifying Direct Variations from Ordered Pairs Tell whether the relationship is a direct variation. Explain. 5) 6) Find y x for each ordered pair. Find y x for each ordered pair. Direct Variation? Constant of Variation: Direct Variation? Constant of Variation: Example 3: Identifying Direct Variations from a Graph Tell whether the relationship is a direct variation. Explain. 7) 8) Direct Variation? Constant of Variation: Direct Variation? Constant of Variation: 48

51 Example 4: Writing and Solving Direct Variation Equations 9) The value of y varies directly with x, and y = 3 when x = 9. Find y when x = 21. Use a proportion: y x ) The value of y varies directly with x, and y = 4.5 when x = 0.5. Find y when x = 10. Challenge SUMMARY 49

52 Exit Ticket Day 8 Homework Direct Variation Tell whether each equation is a direct variation. If so, identify the constant of variation. 2) y = 3x 3) y = 2x 9 3) 2x + 3y = 0 4) 3y = 9x Find the value of y x for each ordered pair. Then tell whether the relationship is a direct variation. 5) 6) 7) 50

53 Tell whether each graph is a direct variation. If so, identify the constant of variation. 8) 9) 10) The value y varies directly with x, and y = 18 when x = 6. Find y when x = 8. 11) The value of y varies directly with x and y = ½ when x = 5. Find y when x = ) 51

54 Chapter 5: Review of Linear Functions Section 1: Slope 52

55 Section 2: X and Y Intercepts 9. Find the x-intercept and the y-intercept for each of the following: a. 3x + y = 6 b. -2x 4y = Find the x-intercept and the y-intercept for each of the following: 53

56 Section 3: Direct Variation Tell whether each is a direct variation. If yes, identify the constant of variation? 54

57 SECTION 4: Writing Equations of Lines 55

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60 Graph Each Vertical and/or Horizontal Line. 30. x = x = y = y =

61 Cost (dollars) t Applications 36. The graph below shows the relationship between the number of miles driven and the cost of Super-City s taxi fare. $16 $14 Super City Taxi Fare $12 $10 $8 $6 $4 $ Number of Miles Driven Part A Write an equation show the relationship between the number of miles driven and the cost of Super-City s taxi fare. Equation: Part B What is the taxi fare for being driven 15 miles? Answer: dollars 59

62 37. The accompanying graph represents the yearly cost of joining a Sports Club. Part A Write an equation show the relationship between the number of months and the yearly cost. Equation: Part B What is the total cost of joining the club and attending 10 months during the year? Answer: dollars 60

63 38. An online video store rents movies for $2.00 per video plus a $5.00 membership fee. Part A Write an equation to represent the cost of renting a video in relationship to the number of videos rented. Equation: Part B Make a table of values to represent your equation in part A. Number of Videos Cost ($) Part C Graph your equation using your table of values. 20 Cost for Video Rentals Cost ($) Number of videos Part D Use the graph to determine the cost for renting 6 videos. Answer: dollars 61

64 $ Cost 39. Mrs. Jackson will need a babysitter for her infant baby. She decides to offer $20 for travel plus $5 per hour worked. Part A Write an equation to represent the cost for a babysitter in relationship to the number of hours worked. Equation: Part B Make a table of values to represent your equation in part A. Number of Hours Cost ($) Part C Graph your equation using your table of values. Number of Hours Part D Determine the cost of hiring a babysitter for 10 hours. Answer: dollars 62

65 40. m = -4, (-2, -8)

66 Section 5: Parallel and Perpendicular Lines

67 (-6, 8) Parallel to x = -2, through (-12, 0) Perpendicular to y = -5, through (1, -2) Parallel to x-axis, through, (3, 8) 65

68 Draw a line parallel to the given line below passing through given point Line 1 Line 1 Draw a line perpendicular to the given line below passing through given point Line 1 Line 1 66