name ________________________________ date … · web view2013-01-08 · algebra . chapter . 5:...

Algebra Chapter 5: LINEAR FUNCTIONS

Name:______________________________ Teacher:____________________________

Pd: _______

Table of ContentsDay 1 - Chapter 5-3/5-4: SlopeSWBAT: Calculate the slope from any two points

Pgs. #1 - 5Hw pgs. #6 – 7

Day 2 - Chapter 5-6: Slope – Intercept FormSWBAT: Write and Graph a linear equation in Slope – Intercept Form

Pgs. #8 – 11Hw pgs. #12 – 14

Day 3 - Chapter 5-7: Point - Slope FormSWBAT: Write and Graph a linear equation in Point - Slope Form

Pgs. #15 – 19Hw pgs. #20 – 21

Day 4 - Chapter 5-6/5-7: Vertical and Horizontal LinesSWBAT: Write and Graph Vertical and Horizontal Lines

Pgs. #22-25Hw 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 LinesSWBAT: Calculate the slope of Parallel and Perpendicular Lines

Pgs. #32-37Hw pgs. #38-39

Day 7 - Chapter 5-8: Equations of Parallel and Perpendicular LinesSWBAT: Write the equation of Parallel and Perpendicular Lines

Pgs. #40-43Hw pgs. #44-45

Day 8 - Chapter 5-5: Direct VariationSWBAT: Identify, write, and graph direct variations

Pgs. #46-50Hw pgs. #50-51

Day 9 – 10: Review of Chapter 5SWBAT: Graph and Write Linear Equations

Pgs. #52-66

Day 1 – Slope

Warm - Up

Find the x- and y- intercepts.

a. b.

x-intercept: _______________ x-intercept: _______________

y-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

1

DEFINITION OF SLOPE

Example 1: Calculating the slope from a Graph

a: Find the slope of the line. b: Find the slope of the line.

1st Point: _________ 2nd Point: ________ 1st Point: _________ 2nd Point: _________

c: Find the slope of the line. d: Find the slope of the line.

1st Point: _________ 2nd Point: _________ 1st Point: ________ 2nd Point: _________

2

y

x

y

x

y

x

y

x

e. f.

Example 2: Calculating the slope from a set up points

a) Find the slope of the line that passes through the points .

3

(8,7 )⏟x 1, y1 and

(4,5 )⏟x2 , y2

(4,3 )⏟x 1 , y1 and

(−5 ,−2 )⏟x 2 , y2

b) Find the slope of the line that passes through the points (4, 3) and (–5, –2).

c) Find the slope of the line that passes through the points (–4, –7) and (–3, –5).

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

(−4 ,−7 )⏟x 1, y 1 and

(−3 ,−5 )⏟x 2 , y 2

Challenge

Summary

Exit Ticket

1. Fill in the blanks.

2.

5

Day 1 – HomeworkSlope

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

c) d)

7

Day 2 - Slope – Intercept Form

Warm Up

Motivation:

Who uses this?

8

Graphing by using slope and y-intercept

1. y=3

4x−2

m = ______ 2. y=−2x+4 m = ______ y-intercept = b = (0, ____ ) y-intercept = b = (0, ____ )

Practice

Graphing by using slope and y-intercept

3. y=1

2x−3

m = ______ 4. y=3 x m = ______y-intercept = b = (0, ____ ) y-intercept = b = (0, ____ )

9

5.

Writing Equations of Graphs

9. Write the equation in slope–intercept form. Then graph the line described by the equation.

3x + 2y = 5

10

6. 7. 8.

10. Write the equation in slope–intercept form. Then graph the line described by the equation.

4x - 2y = 14

Challenge

SUMMARY

Exit Ticket

11

Day 2 – HomeworkSlope – Intercept Form

1) Which of the following lines has a slope of 5 and a y-intercept of ?

(1) (3)

(2) (4)

2) Which of the following equations represents the graph shown?

(1) (3)

(2) (4)

3) Graph each line.

(a) y = –3x+ 2 (b) y = x

12

x

y

(c) y = 6x + 3 (d) y = x + 9

(e) y = –x + 2 (f) y = x - 3

(g) y = -32x - 4 (h) y = 2x + 7

13

1) Write an equation of each line in slope – intercept form. Identify the slope and y-intercept.

a. b.

c. 6x + 2y = 8 d.

14

Day 3 – Point Slope Form

Warm – Up

15

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

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

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 – y1 = m(x – x1)

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 – y1 = m(x – x1)

18

ChallengeWrite the equation of a line in point-slope form passing through the two points given.

(f, g) (h, j)

SUMMARY

Exit Ticket

19

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)

Equation: ______________________

4) slope = –1; (6, –1 )

Equation: ______________________

5) slope = 0; (1, –8)

Equation: ______________________

6) slope = –9; (–2, –3)

Equation: ______________________

20

Write an equation for the line through the two points in slope intercept form. 7) (2, 1); (0, –7)

Equation: ______________________

8) (–6, –6); (2, –2)

Equation: ______________________

9) (–2, –3); (–1, –4)

Equation: ______________________

10) (6, 12); (0, 0)

Equation: ______________________

Write an equation for the line for each graph.

11) 12)

21

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)

4. 5. 6.

22

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)

10. 11. 12.

Parallel LinesParallel Lines have the _______ slope

What can you say about all horizontal lines?

23

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…..13.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 0.

18.Through (3, 3) with an undefined slope.

24

Write the slope-intercept form of the equation of the line through the given points.

1) through: (5, -2) and (0, -2) 2) through: (-6, -1) and (-6, 11)

ChallengeWrite 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)

Exit Ticket

25

1.

2.

Day 4 - HW

26

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

Day 5 – Review of Sections 5-2 through 5-6

28

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

31

Day 6 – Slopes of Parallel and Perpendicular Lines

Warm UpDirections: Find the reciprocal.

1) 2 2)

13 3)

−59

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)

32

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

Challenge

If and the slope of and the slope of is , then find the value of x. Justify algebraically or numerically.

SUMMARY

Exit Ticket

1.

2.

37

Day 6 – Slopes of Parallel and Perpendicular Lines HW

38

7)

8)

9)

10)

39

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(0,8 ) .

1) 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 – y1 = m(x – x1) 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 =

12 x – 7.

Step 1: m = _____


40

Equation: __________________________________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 = _____


Equation: __________________________________

4) Write an equation for the line that passes through (2, 6) and is perpendicular to the line described by

y = -

13 x + 2.

Step 1: m = _____


Equation: __________________________________

41

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

Challenge

SUMMARY

Exit Ticket

1.

2.

43

Day 7 – Equations of Parallel and Perpendicular Lines - HW

44

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

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? _____________ Direct Variation? ____________

Constant of Variation: ___________ Constant of Variation: __________

3) –4x + 3y = 0 4) 3x + 0 = 15y



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

Example 2: Identifying Direct Variations from Ordered Pairs

Tell whether the relationship is a direct variation. Explain.

5) 6)

Find for each ordered pair. Find for each ordered pair.



Example 3: Identifying Direct Variations from a Graph

Tell whether the relationship is a direct variation. Explain.

7) 8)



48

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:

yx=3

9=

10) The value of y varies directly with x, and y = 4.5 when x = 0.5. Find y when x = 10.

Challenge

SUMMARY

49

Exit Ticket

Day 8 – HomeworkDirect 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 for each ordered pair. Then tell whether the relationship is a direct variation.

5) 6) 7)

________________ _________________ _________________

50

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 = 30.

12)

51

Chapter 5: Review of Linear Functions

Section 1: Slope

52

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 = -8

10. Find the x-intercept and the y-intercept for each of the following:

53

Section 3: Direct Variation

11.

12.

13. Tell whether each is a direct variation. If yes, identify the constant of variation?

54

14.

15.

SECTION 4: Writing Equations of Lines

55

16. 17. 18.

19. 20. 21.

22. 23.

24. 25.

56

26. 27.

28. 29.

57

Graph Each Vertical and/or Horizontal Line.

30. x = 3 31. x = -2

32. y = 4 33. y = -3

34. 35.

58

Applications

36. The graph below shows the relationship between the number of miles driven and the cost of Super-City’s taxi fare.

Part AWrite an equation show the relationship between the number of miles driven and the cost of Super-City’s taxi fare.

Equation: __________________

Part BWhat is the taxi fare for being driven 15 miles?

Answer: __________________ dollars

59

Number of Miles Driven

Cost (dollars)t

$16

$14

$12

$10

$8

$6

$4

$2

0 10987654321

Super – City Taxi Fare

37. The accompanying graph represents the yearly cost of joining a Sports Club.

Part AWrite an equation show the relationship between the number of months and the yearly cost.

Equation: __________________

Part BWhat is the total cost of joining the club and attending 10 months during the year?

Answer: _______________ dollars

60

38. An online video store rents movies for $2.00 per video plus a $5.00 membership fee.

Part AWrite an equation to represent the cost of renting a video in relationship to the number of videos rented.

Equation: _____________________________

Part BMake a table of values to represent your equation in part A.

Number of Videos Cost($)

Part CGraph your equation using your table of values.

Part DUse the graph to determine the cost for renting 6 videos.

Answer: __________________ dollars

61

Cost ($)

Cost for Video Rentals

Number of videos6543210

20

18

16

14

12

10

8

6

4

2

39. Mrs. Jackson will need a babysitter for her infant baby. She decides to offer $20 for travel plus $5 per hour worked.

Part AWrite an equation to represent the cost for a babysitter in relationship to the number of hours worked.

Equation: _____________________________

Part BMake a table of values to represent your equation in part A.

Number of Hours Cost($)

Part CGraph your equation using your table of values.

Part DDetermine the cost of hiring a babysitter for 10 hours.

Answer: __________________ dollars

62

$ Cost

Number of Hours

40. m = -4, (-2, -8) 41.

42. 43.

44. 45.

63

Section 5: Parallel and Perpendicular Lines

46. 47.

48. 49.

50. 51.

64

52. 53.

54. 55. Parallel to x = -2, through (-12, 0)

56. 57. Perpendicular to y = -5, through (1, -2)

58. 59. Parallel to x-axis, through, (3, 8)

65

(-6, 8)

Draw a line parallel to the given line below passing through given point.

60. 61.

Draw a line perpendicular to the given line below passing through given point.

62. 63.

66

Line1

Line1

Line1

Line1

name ________________________________ date … · web view2013-01-08 · algebra . chapter . 5:...

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