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  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Key Terms
    13. Key Concepts
    14. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Key Terms
    12. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index

Be Prepared

4.1

2

4.2

16

4.3

5

4.4

−1

4.5

y=123x2y=123x2

4.6

1212

4.7

1212

4.8

0, undefined

4.9

−5,−5,5−5,−5,5

4.10

x+14x+14

4.11

7373

4.12

y=122x−3y=122x−3

4.13

x=103x=103

4.14

25x+625x+6

4.15

x>5x>5

4.16

x is less than 5.

4.17

7

Try It

4.1
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 2, 1) is plotted and labeled "a". The point (negative 3, negative 1) is plotted and labeled "b". The point (4, negative 4) is plotted and labeled "c". The point (negative 4, negative one half) is plotted and labeled “d”.
4.2
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 4, 1) is plotted and labeled "a". The point (negative 2, 3) is plotted and labeled "b". The point (2, negative 5) is plotted and labeled "c". The point (negative 3, 2 and one half) is plotted and labeled “d”.
4.3
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled.
4.4
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (negative 5, 0), (3, 0), (0, 0), (0, negative 1), and (0, 4) are plotted and labeled.
4.5

A: (5,1)(5,1) B: (−2,4)(−2,4) C: (−5,−1)(−5,−1) D: (3,−2)(3,−2) E: (0,−5)(0,−5) F: (4,0)(4,0)

4.6

A: (4,2)(4,2) B: (−2,3)(−2,3) C: (−4,−4)(−4,−4) D: (3,−5)(3,−5) E: (−3,0)(−3,0) F: (0,2)(0,2)

4.7

a, c

4.8

b, c

4.9

b

4.10

a, b

4.11
y=3x1y=3x1
xx yy (x,y)(x,y)
0 −1−1 (0,−1)(0,−1)
−1−1 −4−4 (−1,−4)(−1,−4)
2 5 (2,5)(2,5)
4.12
y=6x+1y=6x+1
xx yy (x,y)(x,y)
0 1 (0,1)(0,1)
1 7 (1,7)(1,7)
−2−2 −11−11 (−2,−11)(−2,−11)
4.13
2x5y=202x5y=20
xx yy (x,y)(x,y)
0 −4−4 (0,−4)(0,−4)
10 0 (10,0)(10,0)
−5−5 −6−6 (−5,−6)(−5,−6)
4.14
3x4y=123x4y=12
xx yy (x,y)(x,y)
0 −3−3 (0,−3)(0,−3)
4 0 (4,0)(4,0)
−4−4 −6−6 (−4,−6)(−4,−6)
4.15

Answers will vary.

4.16

Answers will vary.

4.17

Answers will vary.

4.18

Answers will vary.

4.19

yes, yes  yes, yes

4.20

no, no  yes, yes

4.37

x- intercept: (2,0)(2,0); y- intercept: (0,−2)(0,−2)

4.38

x- intercept: (3,0)(3,0), y- intercept: (0,2)(0,2)

4.39

x- intercept: (4,0)(4,0), y- intercept: (0,12)(0,12)

4.40

x- intercept: (8,0)(8,0), y- intercept: (0,2)(0,2)

4.41

x- intercept: (4,0)(4,0), y- intercept: (0,−3)(0,−3)

4.42

x- intercept: (4,0)(4,0), y- intercept: (0,−2)(0,−2)

4.49

4343

4.50

1414

4.51

2323

4.52

4343

4.57

2525

4.58

3434

4.59

4343

4.60

3535

4.61

5454

4.62

3232

4.63

undefined

4.64

0

4.65

1

4.66

1

4.67

−1−1

4.68

10

4.75

712712

4.76

512512

4.77

136136

4.78

148148

4.79

slope m=23m=23 and y-intercept (0,−1)(0,−1)

4.80

slope m=12m=12 and y-intercept (0,3)(0,3)

4.81

25;(0,−1)25;(0,−1)

4.82

43;(0,1)43;(0,1)

4.83

14;(0,2)14;(0,2)

4.84

32;(0,6)32;(0,6)

4.95

intercepts  horizontal line  slope–intercept  vertical line

4.96

vertical line  slope–intercept  horizontal line  intercepts

4.97
  1. 50 inches
  2. 66 inches
  3. The slope, 2, means that the height, h, increases by 2 inches when the shoe size, s, increases by 1. The h-intercept means that when the shoe size is 0, the height is 50 inches.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable s and runs from negative 2 to 15. The y-axis of the plane represents the variable h and runs from negative 1 to 80. The line begins at the point (0, 50) and goes through the points (8, 66).
4.98
  1. 40 degrees
  2. 65 degrees
  3. The slope, 1414, means that the temperature Fahrenheit (F) increases 1 degree when the number of chirps, n, increases by 4. The T-intercept means that when the number of chirps is 0, the temperature is 40°40°.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from 10 to 140 The y-axis of the plane represents the variable T and runs from negative 5 to 75. The line begins at the point (0, 40) and goes through the point (100, 65).
4.99
  1. $60
  2. $185
  3. The slope, 0.5, means that the weekly cost, C, increases by $0.50 when the number of miles driven, n, increases by 1. The C-intercept means that when the number of miles driven is 0, the weekly cost is $60

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 65) and goes through the point (250, 185).
4.100
  1. $35
  2. $170
  3. The slope, 1.8, means that the weekly cost, C, increases by $1.80 when the number of invitations, n, increases by 1.80.
    The C-intercept means that when the number of invitations is 0, the weekly cost is $35.;

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 35) and goes through the point (75, 170).
4.101

parallel

4.102

parallel

4.103

parallel

4.104

parallel

4.105

parallel

4.106

parallel

4.107

parallel

4.108

not parallel; same line

4.109

perpendicular

4.110

perpendicular

4.111

not perpendicular

4.112

not perpendicular

4.113

y=25x+4y=25x+4

4.114

y=x3y=x3

4.115

y=35x+1y=35x+1

4.116

y=43x5y=43x5

4.117

y=56x2y=56x2

4.118

y=23x4y=23x4

4.119

y=25x1y=25x1

4.120

y=34x4y=34x4

4.121

y=8y=8

4.122

y=4y=4

4.123

y=52x132y=52x132

4.124

y=25x+225y=25x+225

4.125

y=13x103y=13x103

4.126

y=25x235y=25x235

4.127

x=5x=5

4.128

x=−4x=−4

4.129

y=3x10y=3x10

4.130

y=12x+1y=12x+1

4.131

y=13x+103y=13x+103

4.132

y=−2x+16y=−2x+16

4.133

y=−5y=−5

4.134

y=−1y=−1

4.135

x=−5x=−5

4.136

x=−4x=−4

4.137

yes  yes  yes  yes  no

4.138

yes  yes  no  no  yes

4.139

y−2x+3y−2x+3

4.140

y12x4y12x4

4.141

x4y8x4y8

4.142

3xy63xy6

Section 4.1 Exercises

1.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 4, 2) is plotted and labeled "a". The point (negative 1, negative 2) is plotted and labeled "b". The point (3, negative 5) is plotted and labeled "c". The point (negative 3, 5) is plotted and labeled “d”. The point (5 thirds, 2) is plotted and labeled “e”.
3.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (3, negative 1) is plotted and labeled "a". The point (negative 3, 1) is plotted and labeled "b". The point (negative 2, 2) is plotted and labeled "c". The point (negative 4, negative 3) is plotted and labeled “d”. The point (1, 14 fifths) is plotted and labeled “e”.
5.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 2, 0) is plotted and labeled "a". The point (negative 3, 0) is plotted and labeled "b". The point (0, 0) is plotted and labeled "c". The point (0, 4) is plotted and labeled “d”. The point (0, 3) is plotted and labeled “e”.
7.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (0, 0) is plotted and labeled "a". The point (0, negative 3) is plotted and labeled "b". The point (negative 4, 0) is plotted and labeled "c". The point (1, 0) is plotted and labeled “d”. The point (0, negative 2) is plotted and labeled “e”.
9.

A: (−4,1)(−4,1) B: (−3,−4)(−3,−4) C: (1,−3)(1,−3) D: (4,3)(4,3)

11.

A: (0,−2)(0,−2) B: (−2,0)(−2,0) C: (0,5)(0,5) D: (5,0)(5,0)

13.

a, b

15.

a, c

17.

b, c

19.

a, b

21.
xx yy (x,y)(x,y)
0 −4−4 (0,−4)(0,−4)
2 0 (2,0)(2,0)
−1−1 −6−6 (−1,−6)(−1,−6)
23.
xx yy (x,y)(x,y)
0 5 (0,5)(0,5)
3 2 (3,2)(3,2)
−2−2 7 (−2,7)(−2,7)
25.
xx yy (x,y)(x,y)
0 1 (0,1)(0,1)
3 2 (3,2)(3,2)
6 3 (6,3)(6,3)
27.
xx yy (x,y)(x,y)
0 −2−2 (0,−2)(0,−2)
2 −5−5 (2,−5)(2,−5)
−2−2 1 (−2,1)(−2,1)
29.
xx yy (x,y)(x,y)
0 2 (0,2)(0,2)
3 4 (3,1)(3,1)
6 0 (6,0)(6,0)
31.
xx yy (x,y)(x,y)
0 −2−2 (0,−2)(0,−2)
10 2 (10,2)(10,2)
5 0 (5,0)(5,0)
33.

Answers will vary.

35.

Answers will vary.

37.

Answers will vary.

39.

Answers will vary.

41.

Answers will vary.

43.

Answers will vary.

45.

Answers will vary.

47.

Answers will vary.

49.


The graph shows the x y-coordinate plane. The x- and y-axes each run from 0 to 25. The points (0, 7), (2, 11), (4, 15), (6, 16), (8, 19), (10, 20) and (12, 21) are plotted and labeled.


Age and weight are only positive.

51.

Answers will vary.

53.

Answers will vary.

Section 4.2 Exercises

55.

yes; yes  no; no  yes; yes  yes; yes

57.

yes; yes  yes; yes  yes; yes  no; no

59.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 10), (negative 2, negative 7), (negative 1, negative 4), (0, negative 1), (1, 2), (2, 5), and (3, 8).
61.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 3, 8), (negative 2, 6), (negative 1, 4), (0, 2), (1, 0), (2, negative 2), (3, negative 4), (4, negative 6), and (5, negative 8).
63.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, negative 8), (negative 9, negative 7), (negative 8, negative 6), (negative 7, negative 5), (negative 6, negative 4), (negative 5, negative 3), (negative 4, negative 2), (negative 3, negative 1), (negative 2, 0), (negative 1, 1), (0, 2), (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8), (7, 9), and (8, 10).
65.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 7), (negative 9, 6), (negative 8, 5), (negative 7, 4), (negative 6, 3), (negative 5, 2), (negative 4, 1), (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), (4, negative 7), (5, negative 8), (6, negative 9), and (7, negative 10).
67.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 5, negative 10), (negative 4, negative 8), (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10).
69.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, 12), (negative 2, 8), (negative 1, 4), (0, 0), (1, negative 4), (2, negative 8), and (3, negative 12).
71.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 12, negative 4), (negative 10, negative 3), (negative 8, negative 2), (negative 6, negative 1), (negative 4, 0), (negative 2, 1), (0, 2), (2, 3), (4, 4), (6, 5), (8, 6), and (10, 7).
73.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 9), (0, negative 5), (3, negative 1), (6, 3), and (9, 7).
75.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 5), (negative 5, 3), (0, 1), (5, negative 1), and (10, negative 3).
77.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 6, 11), (negative 4, 8), (negative 2, 5), (0, 2), (2, negative 1), (4, negative 4), (6, negative 7), and (8, negative 10).
79.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 3, 9), (negative 2, 8), (negative 1, 7), (0, 6), (1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 0), (7, negative 1), (8, negative 2), (9, negative 3), and (10, negative 4).
81.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 7), (negative 9, 6), (negative 8, 5), (negative 7, 4), (negative 6, 3), (negative 5, 2), (negative 4, 1), (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), (4, negative 7), (5, negative 8), (6, negative 9), and (7, negative 10).
83.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 8, negative 10), (negative 7, negative 9), (negative 6, negative 8), (negative 5, negative 7), (negative 4, negative 6), (negative 3, negative 5), (negative 2, negative 4), (negative 1, negative 3), (0, negative 2), (1, negative 1), (2, 0), (3, 1), (4, 2), (5, 3), (6, 4), (7, 5), (8, 6), (9, 7), and (10, 8).
85.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 9, negative 8), (negative 8, negative 7), (negative 7, negative 6), (negative 6, negative 5), (negative 5, negative 4), (negative 4, negative 3), (negative 3, negative 2), (negative 2, negative 1), (negative 1, 0), (0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), and (9, 10).
87.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to -7. The equation 3 x plus y equals 7 is graphed.
89.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 5, 7), (negative 4, 5), (negative 3, 3), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 5), and (2, negative 7).
91.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 4), (negative 3, 3), (0, 2), (3, 1), and (6, 0).
93.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 5, negative 2), (0, negative 4), and (5, negative 6).
95.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 3, 6), (0, 4), (3, 2), and (6, 0).
97.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 4, negative 6), (0, negative 3), (4, 0), and (8, 3).
99.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative three halves), (negative 3, negative 1), (0, negative one half), (3, 0), and (6, one half).
101.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, 7), (0, 2), (2, negative 3), and (4, negative 8).
103.
The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (4, 0), (4, 1), (4, 2) and all points with first coordinate 4.
105.
The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (negative 2, 0), (negative 2, 1), (negative 2, 2) and all points with first coordinate negative 2.
107.
The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, 3), (1, 3), (2, 3) and all points with second coordinate 3.
109.
The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, negative 5), (1, negative 5), (2, negative 5) and all points with second coordinate negative 5.
111.
The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (7/3, 0), (7/3, 1), (7/3, 2) and all points with first coordinate 7/3.
113.
The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The horizontal line goes through the points (0, negative 15/4), (1, negative 15/4), (2, negative 15/4) and all points with second coordinate negative 15/4.
115.
The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. One line is a straight horizontal line going through the points (negative 4, 2) (0, 2), (4, 2), and all other points with second coordinate 2. The other line is a slanted line going through the points (negative 5, negative 10), (negative 4, negative 8), (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10).
117.
The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. One line is a straight horizontal line going through the points (negative 4, negative one half) (0, negative one half), (4, negative one half), and all other points with second coordinate negative one half. The other line is a slanted line going through the points (negative 10, 5), (negative 8, 4), (negative 6, 3), (negative 4, 2), (negative 2, 1), (0, 0), (1, negative 2), (2, negative 4), (3, negative 6), (4, negative 8), and (5, negative 10).
119.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, negative 8), (negative 1, negative 4), (0, 0), (1, 4), and (2, 8).
121.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 6), (negative 4, 5), (negative 2, 4), (0, 3), (2, 2), (4, 1), and (6, 0).
123.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 6), (negative 5, 5), (negative 4, 4), (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, negative 1), (2, negative 2), (3, negative 3), (4, negative 4), (5, negative 5), and (6, negative 6).
125.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 3, negative 7), (negative 2, negative 6), (negative 1, negative 4), (0, negative 3), (1, negative 2), (2, negative 1), (3, 0), (4, 1), (5, 2), and (6, 3).
127.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, 6), (negative 1, 4), (0, 2), (1, negative 2), and (2, negative 6).
129.
The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The horizontal line goes through the points (0, negative 1), (1, negative 1), (2, negative 1) and all points with second coordinate negative 1.
131.
The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 4), (negative 3, 3), (0, 2), (3, 1), and (6, 0).
133.
The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The vertical line goes through the points (3, 0), (3, 1), (3, 2) and all points with first coordinate 3.
135.

$722, $850, $978

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from 0 to 1200 in increments of 100. The y-axis of the plane runs from 0 to 1000 in increments of 100. The straight line starts at the point (0, 594) and goes through the points (400, 722), (800, 850), and (1200, 978). The right end of the line has an arrow pointing up and to the right.
137.

Answers will vary.

Section 4.3 Exercises

139.

(3,0),(0,3)(3,0),(0,3)

141.

(5,0),(0,−5)(5,0),(0,−5)

143.

(−2,0),(0,−2)(−2,0),(0,−2)

145.

(−1,0),(0,1)(−1,0),(0,1)

147.

(6,0),(0,3)(6,0),(0,3)

149.

(0,0)(0,0)

151.

(4,0),(0,4)(4,0),(0,4)

153.

(−2,0),(0,−2)(−2,0),(0,−2)

155.

(5,0),(0,−5)(5,0),(0,−5)

157.

(−3,0),(0,3)(−3,0),(0,3)

159.

(8,0),(0,4)(8,0),(0,4)

161.

(2,0),(0,6)(2,0),(0,6)

163.

(12,0),(0,−4)(12,0),(0,−4)

165.

(2,0),(0,−8)(2,0),(0,−8)

167.

(5,0),(0,2)(5,0),(0,2)

169.

(4,0),(0,−6)(4,0),(0,−6)

171.

(−3,0),(0,1)(−3,0),(0,1)

173.

(−10,0),(0,2)(−10,0),(0,2)

175.

(0,0)(0,0)

177.

(0,0)(0,0)

179.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The line graphed is negative x plus 5 y equals 10.
181.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 8, 6), (negative 6, 5), (negative 4, 4), (negative 2, 3), (0, 2), (2, 1), (4, 0), (6, negative 1), (8, negative 2), and (10, negative 3).
183.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 8, 10), (negative 7, 9), (negative 6, 8),(negative 5, 7), (negative 4, 6), (negative 3, 5), (negative 2, 4), (negative 1, 3), (0, 2), (1, 1), (2, 0), (3, negative 1), (4, negative 2), (5, negative 3), (6, negative 4), (7, negative 5), (8, negative 6), (9, negative 7), and (10, negative 8).
185.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 7 to 7. The y- axis of the planes runs from negative 7 to 7. The straight line goes through the points (negative 7, 4), (negative 6, 3), (negative 5, 2),(negative 4, 1), (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), and (4, negative 7).
187.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 8, negative 9), (negative 7, negative 8), (negative 6, negative 7),(negative 5, negative 6), (negative 4, negative 5), (negative 3, negative 4), (negative 2, negative 3), (negative 1, negative 2), (0, negative 1), (1, 0), (2, 1), (3, 2), (4, 3), (5, 4), (6, 5), (7, 6), (8, 7), (9, 8), and (10, 9).
189.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 8, negative 4), (negative 7, negative 3), (negative 6, negative 2),(negative 5, negative 1), (negative 4, 0), (negative 3, 1), (negative 2, 2), (negative 1, 3), (0, 4), (1, 5), (2, 6), (3, 7), (4, 8), (5, 9), (6, 10), (7, 11), and (8, 12).
191.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 2, 12), (negative 1, 8), (0, 4), (1, 0), (2, negative 4), (3, negative 8), and (4, negative 12).
193.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 7 to 7. The y- axis of the planes runs from negative 7 to 7. The straight line goes through the points (negative 6, 6), (negative 4, 5), (negative 2, 4), (0, 3), (2, 2), (4, 1), and (6, 0).
195.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 6, negative 12), (negative 4, negative 9), (negative 2, negative 6), (0, negative 3), (2, 0), (4, 3), (6, 6), (8, 9), and (10, 12).
197.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 10, 0), (negative 5, 2), (0, 4), (5, 6), and (10, 8).
199.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 6, negative 12), (negative 5, negative 9), (negative 4, negative 6), (negative 3, negative 3), (negative 2, 0), (1, 3), (2, 6), (3, 9), and (4, 12).
201.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 5, 10), (negative 4, 8), (negative 3, 6), (negative 2, 4), (negative 1, 2), (0, 0), (1, negative 2), (2, negative 4), (3, negative 6), (4, negative 8), (5, negative 10), and (6, negative 12)
203.
The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 10, 10), (negative 9, 9), (negative 8, 8), (negative 7, 7), (negative 6, 6), (negative 5, 5), (negative 4, 4), (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8), (9, 9), and (10, 10)
205.

(0,1000),(15,0)(0,1000),(15,0)
At (0,1000)(0,1000), he has been gone 0 hours and has 1000 miles left. At (15,0)(15,0), he has been gone 15 hours and has 0 miles left to go.

207.

Answers will vary.

209.

Answers will vary.

Section 4.4 Exercises

211.

1414

213.

2323

215.

−32=32−32=32

217.

3434

219.
The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 2, row 5 and the peg in column 5, row 3, forming a line.
221.
The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 4 and the peg in column 5, row 3, forming a line.
223.
The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 4 and the peg in column 3, row 5, forming a line.
225.
The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 2 and the peg in column 4, row 4, forming a line.
227.

2525

229.

5454

231.

1313

233.

3434

235.

3434

237.

−3−3

239.

2323

241.

1414

243.

0

245.

undefined

247.

0

249.

undefined

251.

5252

253.

3434

255.

5252

257.

8787

259.

7373

261.

−1−1

263.
The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (1, negative 2) and (5, 1).
265.
The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (2, 5) and (5, 4).
267.
The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 3, 4) and (negative 1, 1).
269.
The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 1, negative 4) and intercepts the x-axis at (2, 0).
271.
The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line intercepts the y-axis at (0, 3) and passes through the point (5, 1).
273.
The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line intercepts the x-axis at (negative 2, 0) and passes through the point (2, 3).
275.
The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 3, 3) and (negative 2, 5).
277.
The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (1, 5) and (2, 2).
279.

1313 4 12 pitch or 4-in-12 pitch

281.

350350; rise = 3, run = 50

283.

288 inches (24 feet)  Models will vary.

285.

When the slope is a positive number the line goes up from left to right. When the slope is a negative number the line goes down from left to right.

287.

A vertical line has 0 run and since division by 0 is undefined the slope is undefined.

Section 4.5 Exercises

289.

slope m=4m=4 and y-intercept (0,−2)(0,−2)

291.

slope m=−3m=−3 and y-intercept (0,1)(0,1)

293.

slope m=25m=25 and y-intercept (0,3)(0,3)

295.

−9;(0,7)−9;(0,7)

297.

4;(0,−10)4;(0,−10)

299.

−4;(0,8)−4;(0,8)

301.

83;(0,4)83;(0,4)

303.

73;(0,−3)73;(0,−3)

305.
The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).
307.
The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).
309.
The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).
311.
The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).
313.
The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).
315.
The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).
317.
The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).
319.
The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).
321.

horizontal line

323.

vertical line

325.

slope–intercept

327.

intercepts

329.

slope–intercept

331.

horizontal line

333.

intercepts

335.

slope–intercept

337.
  1. $28
  2. $66.10
  3. The slope, 2.54, means that Randy’s payment, P, increases by $2.54 when the number of units of water he used, w, increases by 1. The P–intercept means that if the number units of water Randy used was 0, the payment would be $28.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).
339.
  1. $15
  2. $143
  3. The slope, 0.32, means that the cost, C, increases by $0.32 when the number of miles driven, m, increases by 1. The C-intercept means that if Janelle drives 0 miles one day, the cost would be $15.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).
341.
  1. $750
  2. $2418.60
  3. The slope, 0.09, means that Patel’s salary, S, increases by $0.09 for every $1 increase in his sales. The S-intercept means that when his sales are $0, his salary is $750.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).
343.
  1. $2850
  2. $4950
  3. The slope, 42, means that the cost, C, increases by $42 for when the number of guests increases by 1. The C-intercept means that when the number of guests is 0, the cost would be $750.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).
345.

parallel

347.

parallel

349.

not parallel

351.

parallel

353.

parallel

355.

parallel

357.

parallel

359.

parallel

361.

not parallel

363.

not parallel

365.

not parallel

367.

not parallel

369.

not parallel

371.

perpendicular

373.

perpendicular

375.

not perpendicular

377.

not perpendicular

379.

perpendicular

381.

perpendicular

383.
  1. For every increase of one degree Fahrenheit, the number of chirps increases by four.
  2. There would be −160−160 chirps when the Fahrenheit temperature is 0°0°. (Notice that this does not make sense; this model cannot be used for all possible temperatures.)
385.

Answers will vary.

Section 4.6 Exercises

387.

y=4x+1y=4x+1

389.

y=8x6y=8x6

391.

y=x+7y=x+7

393.

y=−3x1y=−3x1

395.

y=15x5y=15x5

397.

y=23x3y=23x3

399.

y=2y=2

401.

y=−4xy=−4x

403.

y=−2x+4y=−2x+4

405.

y=34x+2y=34x+2

407.

y=32x1y=32x1

409.

y=6y=6

411.

y=38x1y=38x1

413.

y=56x+2y=56x+2

415.

y=35x+1y=35x+1

417.

y=13x11y=13x11

419.

y=4y=4

421.

y=−7y=−7

423.

y=52x22y=52x22

425.

y=−4x11y=−4x11

427.

y=−8y=−8

429.

y=−4x+13y=−4x+13

431.

y=x+5y=x+5

433.

y=13x143y=13x143

435.

y=7x+22y=7x+22

437.

y=67x+47y=67x+47

439.

y=15x2y=15x2

441.

x=4x=4

443.

x=−2x=−2

445.

y=2y=2

447.

y=−3y=−3

449.

y=4xy=4x

451.

y=12x+32y=12x+32

453.

y=5y=5

455.

y=3x1y=3x1

457.

y=−3x+3y=−3x+3

459.

y=2x6y=2x6

461.

y=23x+5y=23x+5

463.

x=−3x=−3

465.

x=4x=4

467.

y=−4y=−4

469.

y=−1y=−1

471.

y=xy=x

473.

y=32x1y=32x1

475.

y=34x14y=34x14

477.

y=54xy=54x

479.

x=−5x=−5

481.

y=1y=1

483.

y=x+5y=x+5

485.

y=56x+2y=56x+2

487.

y=23x+5y=23x+5

489.

y=35x+1y=35x+1

491.

y=2y=2

493.

y=2x+4y=2x+4

495.

x=−3x=−3

497.

y=13x143y=13x143

499.

y=34xy=34x

501.

y=1.2x+5.2y=1.2x+5.2

503.

Answers will vary.

Section 4.7 Exercises

505.

yes  yes  no  yes  yes

507.

yes  no  yes  yes  yes

509.

no  no  no  yes  yes

511.

y<2x4y<2x4

513.

y13x2y13x2

515.

x+y3x+y3

517.

x+2y−2x+2y−2

519.

2xy<42xy<4

521.

4x3y>124x3y>12

523.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals three-fifths x plus 2 is plotted as a dashed line extending from the bottom left toward the top right. The region below the line is shaded.
525.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative one-third x minus 2 is plotted as a solid line extending from the top left toward the bottom right. The region below the line is shaded.
527.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x minus y equals negative 2 is plotted as a solid line extending from the bottom left toward the top right. The region below the line is shaded.
529.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x plus 5 y equals negative 5 is plotted as a dashed line extending from the top left toward the bottom right. The region below the line is shaded.
531.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 4 x plus 2 y equals negative 8 is plotted as a solid line extending from the top left toward the bottom right. The region to the right of the line is shaded.
533.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals x is plotted as a solid line extending from the bottom left toward the top right. The region above the line is shaded.
535.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 3 x is plotted as a solid line extending from the top left toward the bottom right. The region to the left of the line is shaded.
537.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 1 is plotted as a dashed horizontal line. The region below the line is shaded.
539.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals 2 is plotted as a solid horizontal line. The region above the line is shaded.
541.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x equals negative 2 is plotted as a dashed vertical line. The region to the right of the line is shaded.
543.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x equals 4 is plotted as a solid vertical line. The region to the left of the line is shaded.
545.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x minus y equals negative 3 is plotted as a dashed line extending from the bottom left toward the top right. The region above the line is shaded.
547.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals five-fourths x is plotted as a solid line extending from the bottom left toward the top right. The region below the line is shaded.
549.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 3 x minus 4 is plotted as a dashed line extending from the top left toward the bottom right. The region to the left of the line is shaded.
551.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x equals negative 0 is plotted as a solid vertical line along the y-axis. The region to the right of the line is shaded.
553.

  1. The graph shows the x y-coordinate plane. The x- axis runs from 0 to 20 and the y-axis runs from 0 to 30. The line 2 x plus one-half y equals 20 is plotted as a solid line extending from the top left toward the bottom right. The region below the line is shaded.
  2. Answers will vary.

Review Exercises

557.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (4, 3) is plotted and labeled "a". The point (negative 4, 3) is plotted and labeled "b". The point (negative 4, negative 3) is plotted and labeled "c". The point (4, negative 3) is plotted and labeled “d”.
559.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (2, three halves) is plotted and labeled "a". The point (3, four thirds) is plotted and labeled "b". The point (one third, negative 4) is plotted and labeled "c". The point (one-half, negative 5) is plotted and labeled “d”.
561.

(2,0)(2,0) (0,−5)(0,−5) (−4.0)(−4.0) (0,3)(0,3)

563.

a, b

565.
xx yy (x,y)(x,y)
0 3 (0,3)(0,3)
4 1 (4, 1)
−2−2 4 (−2,4)(−2,4)
567.
xx yy (x,y)(x,y)
0 33 (0,3)(0,3)
2 0 (2,0)(2,0)
−2−2 66 (−2,6)(−2,6)
569.

Answers will vary.

571.

Answers will vary.

573.

yes; yes  yes; yes  yes; yes  no; no

575.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals negative 3 x is plotted as an arrow extending from the top left toward the bottom right.
577.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line x minus y equals 6 is plotted as an arrow extending from the bottom left toward the top right.
579.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line 3 x minus 2 y equals 6 is plotted as an arrow extending from the bottom left toward the top right.
581.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line x equals 3 is plotted as a vertical line.
583.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals four-thirds x is plotted as an arrow extending from the bottom left toward the top right. The line y equals four-thirds is plotted as a horizontal line.
585.

(3,0),(0,3)(3,0),(0,3)

587.

(−1,0),(0,1)(−1,0),(0,1)

589.

(6,0),(0,4)(6,0),(0,4)

591.

(0,0)(0,0)

593.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line x plus y equals negative 2 is plotted as an arrow extending from the top left toward the bottom right.
595.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line 2 x minus y equals 5 is plotted as an arrow extending from the bottom left toward the top right.
597.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals 2 x is plotted as an arrow extending from the bottom left toward the top right.
599.

4343

601.

2323

603.
The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 5 and the point in column 3 row 2.
605.
The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 2 row 2 and the point in column 3 row 3.
607.

1

609.

1212

611.

undefined

613.

0

615.

−6−6

617.

5252

619.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. A line passing through the points (negative 3, 4) and (0, 3) is plotted.
621.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. A line passing through the points (0, 1) and (4, negative 2) is plotted.
623.

110110

625.

slope m=23m=23 and y-intercept (0,4)(0,4)

627.

53;(0,−6)53;(0,−6)

629.

45;(0,85)45;(0,85)

631.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals negative x minus 1 is plotted from the top left to the bottom right.
633.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line 4 x minus 3 y equals 12 is plotted from the bottom left to the top right.
635.

horizontal line

637.

intercepts

639.

plotting points

641.

−$250  $450  The slope, 35, means that Marjorie’s weekly profit, P, increases by $35 for each additional student lesson she teaches. The P–intercept means that when the number of lessons is 0, Marjorie loses $250. 

The graph shows the x y-coordinate plane where h is plotted along the x-axis and P is potted along the y-axis. The x-axis runs from 0 to 24. The y-axis runs from negative 300 to 500. The line P equals 35 h minus 250 is plotted from the bottom left to the top right.
643.

not parallel

645.

perpendicular

647.

y=−5x3y=−5x3

649.

y=−2xy=−2x

651.

y=−3x+5y=−3x+5

653.

y=−4y=−4

655.

y=35xy=35x

657.

y=−2x5y=−2x5

659.

y=12x52y=12x52

661.

y=2y=2

663.

y=25x+8y=25x+8

665.

y=3y=3

667.

y=32x6y=32x6

669.

y=1y=1

671.

yes  no  yes  yes  no

673.

y23x3y23x3

675.

x2y>6x2y>6

677.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals negative one-fourth x plus 3 is plotted as a solid line extending from the top left toward the bottom right. The region below the line is shaded.
679.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line 3 x plus 2 y equals 10 is plotted as a dashed line extending from the top left toward the bottom right. The region above the line is shaded.
681.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals 6 is plotted as a dashed, horizontal line. The region below the line is shaded.

Practice Test

683.

yes  yes  no

685.

(3,0),(0,−4)(3,0),(0,−4)

687.

undefined

689.

11

691.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals five-thirds x minus 1 is plotted. The line passes through the points (0, negative 1) and (three-fifths, 0).
693.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line x minus y equals 2 is plotted. The line passes through the points (0, negative 2) and (2, 0).
695.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals 2 is plotted as a horizontal line passing through the point (0, 2).
697.

y=34x2y=34x2

699.

y=12x4y=12x4

701.

y=45x5y=45x5

703.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals three-halves x plus 5 is plotted. The dashed line passes through the points (0, 5) and (2, 8).
705.
The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals negative 5 x is plotted. The solid line passes through the points (0, 0) and (1, negative 5).
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