Lines, section 1.2 PDF

Preview

Summary

Slope of a Line

Equation of a Line

Intercepts of Lines

Parallel and Perpendicular Lines ...

Description

SECTION 1.2 Lines

Section 1.2:    

Lines

Slope of a Line Equation of a Line Intercepts of Lines Parallel and Perpendicular Lines

Slope of a Line

MATH 1310 College Algebra

27

CHAPTER 1 An Introduction to Graphs and Lines

Solution:

28

University of Houston Department of Mathematics

SECTION 1.2 Lines

MATH 1310 College Algebra

29

CHAPTER 1 An Introduction to Graphs and Lines

Additional Example 1:

Solution:

Additional Example 2:

Solution:

30

University of Houston Department of Mathematics

SECTION 1.2 Lines

Additional Example 3:

Solution:

Additional Example 4:

MATH 1310 College Algebra

31

CHAPTER 1 An Introduction to Graphs and Lines

Solution:

32

University of Houston Department of Mathematics

SECTION 1.2 Lines

Equation of a Line

Solution:

MATH 1310 College Algebra

33

CHAPTER 1 An Introduction to Graphs and Lines

Solution:

34

University of Houston Department of Mathematics

SECTION 1.2 Lines

Solution:

Solution:

MATH 1310 College Algebra

35

CHAPTER 1 An Introduction to Graphs and Lines

Additional Example 1:

Solution:

36

University of Houston Department of Mathematics

SECTION 1.2 Lines

Additional Example 2:

Solution:

MATH 1310 College Algebra

37

CHAPTER 1 An Introduction to Graphs and Lines

Additional Example 3:

Solution:

38

University of Houston Department of Mathematics

SECTION 1.2 Lines

Additional Example 4:

Solution:

MATH 1310 College Algebra

39

CHAPTER 1 An Introduction to Graphs and Lines

Intercepts of Lines

40

University of Houston Department of Mathematics

SECTION 1.2 Lines

MATH 1310 College Algebra

41

CHAPTER 1 An Introduction to Graphs and Lines

Solution:

42

University of Houston Department of Mathematics

SECTION 1.2 Lines

Solution:

MATH 1310 College Algebra

43

CHAPTER 1 An Introduction to Graphs and Lines

Additional Example 1:

Solution:

44

University of Houston Department of Mathematics

SECTION 1.2 Lines

Additional Example 2:

Solution:

MATH 1310 College Algebra

45

CHAPTER 1 An Introduction to Graphs and Lines

Additional Example 3:

Solution:

46

University of Houston Department of Mathematics

SECTION 1.2 Lines

Parallel and Perpendicular Lines

MATH 1310 College Algebra

47

CHAPTER 1 An Introduction to Graphs and Lines

Solution:

48

University of Houston Department of Mathematics

SECTION 1.2 Lines

Solution:

MATH 1310 College Algebra

49

CHAPTER 1 An Introduction to Graphs and Lines

Additional Example 1:

Solution:

Additional Example 2:

Solution:

50

University of Houston Department of Mathematics

SECTION 1.2 Lines

Additional Example 3:

Solution:

Additional Example 4:

Solution:

MATH 1310 College Algebra

51

CHAPTER 1 An Introduction to Graphs and Lines

52

University of Houston Department of Mathematics

Exercise Set 1.2: Lines State whether the slope of each of the following lines is positive, negative, zero, or undefined. 1.

p

2.

q

3.

s

5.

t

6.

w

19.

y

q

y

8

r

2

6

r

4.

Write an equation for each of the following lines.

x

4

−4

2

−2

2 −2

x

−8 −6 −4 −2 −2

2

4

6

8

4

−4

t

−4

−6

−6

w

−8

s

10

p

y

20. 4

2

Find the slope of the line that passes through the following points. If it is undefined, state ‘undefined.’

x

7.

(0, 0) and (3, 7)

8.

(8, 0) and (3, 5)

9.

(2, 5) and ( 4, 10)

−2

2

4

−2

10. (7, 3) and (5, 9)

y

21.

11. ( −2, 3) and (6, − 7)

x

12. ( −1, − 6) and ( −5, 10)

−6

−4

−2

2

13. (3, − 8) and (3, − 4)

−2

14. (8, − 7) and ( −1, − 7) −4

Find the slope of each of the following lines.

15. c

e

6

y 4 3

16. d 17. e 18. f

c

y

22.

4

2 1 −5 −4 −3 −2 −1 −1

x 1

2

3

4

2

5 x

−2

−4

−2

2

4

−3

f

−4

−2

5

d

MATH 1310 College Algebra

−4

53

Exercise Set 1.2: Lines Write each of the following equations in slopeintercept form, identify the slope and y-intercept, and then draw its graph. 23. 2 x + y = 5 24. 3 x − y = −6 25. x + 4 y = 0 26. 2 x + 5 y = 10 27. 4 x − 3y + 9 = 0 28. − 23 x + 12 y = −1 Write an equation of the line that satisfies the given conditions. 29. Slope -

4 ; y -intercept 3 7

47. Passes through (5, -7); parallel to the line y = −5 x + 3 48. Passes through (5, -7); perpendicular to the line y = −5 x + 3 49. Passes through (2, 3); parallel to the line 5 x −2 y = 6 50. Passes through (-1, 5); parallel to the line 4x+3y = 8 51. Passes through (2, 3); perpendicular to the line 5 x −2 y = 6 52. Passes through (-1, 5); perpendicular to the line 4x+3y = 8 53. Passes through (4, -6); parallel to the line containing (3, -5) and (2, 1)

30. Slope − 4 ; y -intercept 5 2 31. Slope ; passes through (-6 4) 3

32. Slope −

5 ; passes through (8, -3) 2

33. Slope −

2 ; passes through (-3, 2) 9

34. Slope

1 ; passes through (-4, -2) 5

35. Passes through (-5, 2) and (-4, -6) 36. Passes through (2, 11) and (-3, 1) 37. Passes through (-4, 5) and (1, -2) 38. Passes through (7, 0) and (3, -5) 39. x-intercept 7; y -intercept -5 40. x-intercept -2; y-intercept 6 41. Slope − 42. Slope

3 ; x-intercept 4 2

1 ; x-intercept -6 5

43. Passes through (1, 4); parallel to the x-axis 44. Passes through (1, 4); parallel to the y -axis 45. Passes through (2, -6); parallel to the line x =4 46. Passes through (2, -6); parallel to the line y =4

54

54. Perpendicular to the line containing (4, -2) and (10, 4); passes through the midpoint of the line segment connecting these points. Answer the following. 55. Sketch the line with slope

2 3

that passes through

the point (3, -4), and then find its equation.

56. Determine whether or not the following points are collinear by using the slope formula: (a) A(-3, 4), B(3, 8), C(6, 10) (b) D(-2, -5), E(0, -3), F(3, 1) 57. Use slopes to show that the following vertices represent the vertices of a parallelogram: A(-3, 4), B(0, 8), C(5, 2), D(2, -2) 58. Use slopes to show that the following vertices represent the vertices of a rectangle: A(-2, -3), B(1, 4), C(-6, 7), D(-9, 0) Answer the following, assuming that each situation can be modeled by a linear equation. 59. If a company can make 21 computers for $23,000, and can make 40 computers for $38,200, write an equation that represents the cost of x computers. 60. A certain electrician charges a $40 traveling fee, and then charges $55 per hour of labor. Write an equation that represents the cost of a job that takes x hours.

University of Houston Department of Mathematics...