Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis

Be Prepared

4.1

2

4.2

16

4.3

5

4.4

−1

4.5

$y = \frac{12 - 3 x}{2}$

4.6

$- \frac{1}{2}$

4.7

$- \frac{1}{2}$

4.8

0, undefined

4.9

$−5, −5, 5$

4.10

$\frac{x + 1}{4}$

4.11

$\frac{7}{3}$

4.12

$y = \frac{12 - 2 x}{−3}$

4.13

$x = \frac{10}{3}$

4.14

$- \frac{2}{5} x + 6$

4.15

$x > 5$

4.16

x is less than 5.

4.17

7

Try It

4.1

4.2

4.3

4.4

4.5

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

4.6

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

4.7

a, c

4.8

b, c

4.9

b

4.10

a, b

4.11

$y = 3 x - 1$
$x$	$y$	$(x, y)$
0	$−1$	$(0, −1)$
$−1$	$−4$	$(−1, −4)$
2	5	$(2, 5)$

4.12

$y = 6 x + 1$
$x$	$y$	$(x, y)$
0	1	$(0, 1)$
1	7	$(1, 7)$
$−2$	$−11$	$(−2, −11)$

4.13

$2 x - 5 y = 20$
$x$	$y$	$(x, y)$
0	$−4$	$(0, −4)$
10	0	$(10, 0)$
$−5$	$−6$	$(−5, −6)$

4.14

$3 x - 4 y = 12$
$x$	$y$	$(x, y)$
0	$−3$	$(0, −3)$
4	0	$(4, 0)$
$−4$	$−6$	$(−4, −6)$

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

4.21

4.22

4.23

4.24

4.25

4.26

4.27

4.28

4.29

4.30

4.31

4.32

4.33

4.34

4.35

4.36

4.37

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

4.38

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

4.39

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

4.40

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

4.41

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

4.42

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

4.43

4.44

4.45

4.46

4.47

4.48

4.49

$\frac{4}{3}$

4.50

$\frac{1}{4}$

4.51

$- \frac{2}{3}$

4.52

$- \frac{4}{3}$

4.53

4.54

4.55

4.56

4.57

$\frac{2}{5}$

4.58

$\frac{3}{4}$

4.59

$- \frac{4}{3}$

4.60

$- \frac{3}{5}$

4.61

$\frac{5}{4}$

4.62

$\frac{3}{2}$

4.63

undefined

4.64

0

4.65

1

4.66

1

4.67

$−1$

4.68

10

4.69

4.70

4.71

4.72

4.73

4.74

4.75

$\frac{7}{12}$

4.76

$\frac{5}{12}$

4.77

$- \frac{1}{36}$

4.78

$- \frac{1}{48}$

4.79

slope $m = \frac{2}{3}$ and y-intercept $(0, −1)$

4.80

slope $m = \frac{1}{2}$ and y-intercept $(0, 3)$

4.81

$\frac{2}{5}; (0, −1)$

4.82

$- \frac{4}{3}; (0, 1)$

4.83

$- \frac{1}{4}; (0, 2)$

4.84

$- \frac{3}{2}; (0, 6)$

4.85

4.86

4.87

4.88

4.89

4.90

4.91

4.92

4.93

4.94

4.95

ⓐ intercepts ⓑ horizontal line ⓒ slope–intercept ⓓ vertical line

4.96

ⓐ vertical line ⓑ slope–intercept ⓒ horizontal line ⓓ intercepts

4.97

ⓐ 50 inches
ⓑ 66 inches
ⓒ 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.
ⓓ

4.98

ⓐ 40 degrees
ⓑ 65 degrees
ⓒ The slope, $\frac{1}{4}$ , 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 $40 °$ .
ⓓ

4.99

ⓐ $60
ⓑ $185
ⓒ 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
ⓓ

4.100

ⓐ $35
ⓑ $170
ⓒ The slope, 1.8, means that the weekly cost, C, increases by $1.80 when the number of invitations, n, increases by 1.
The C-intercept means that when the number of invitations is 0, the weekly cost is $35.;
ⓓ

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

$y = \frac{2}{5} x + 4$

4.114

$y = − x - 3$

4.115

$y = \frac{3}{5} x + 1$

4.116

$y = \frac{4}{3} x - 5$

4.117

$y = \frac{5}{6} x - 2$

4.118

$y = \frac{2}{3} x - 4$

4.119

$y = - \frac{2}{5} x - 1$

4.120

$y = - \frac{3}{4} x - 4$

4.121

$y = 8$

4.122

$y = 4$

4.123

$y = \frac{5}{2} x - \frac{13}{2}$

4.124

$y = - \frac{2}{5} x + \frac{22}{5}$

4.125

$y = \frac{1}{3} x - \frac{10}{3}$

4.126

$y = - \frac{2}{5} x - \frac{23}{5}$

4.127

$x = 5$

4.128

$x = −4$

4.129

$y = 3 x - 10$

4.130

$y = \frac{1}{2} x + 1$

4.131

$y = - \frac{1}{3} x + \frac{10}{3}$

4.132

$y = −2 x + 16$

4.133

$y = −5$

4.134

$y = −1$

4.135

$x = −5$

4.136

$x = −4$

4.137

ⓐ yes ⓑ yes ⓒ yes ⓓ yes ⓔ no

4.138

ⓐ yes ⓑ yes ⓒ no ⓓ no ⓔ yes

4.139

$y \geq −2 x + 3$

4.140

$y \leq \frac{1}{2} x - 4$

4.141

$x - 4 y \leq 8$

4.142

$3 x - y \leq 6$

4.143

4.144

4.145

4.146

4.147

4.148

4.149

4.150

Section 4.1 Exercises

1.

3.

5.

7.

9.

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

11.

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

13.

a, b

15.

a, c

17.

b, c

19.

a, b

21.

$x$	$y$	$(x, y)$
0	$−4$	$(0, −4)$
2	0	$(2, 0)$
$−1$	$−6$	$(−1, −6)$

23.

$x$	$y$	$(x, y)$
0	5	$(0, 5)$
3	2	$(3, 2)$
$−2$	7	$(−2, 7)$

25.

$x$	$y$	$(x, y)$
0	1	$(0, 1)$
3	2	$(3, 2)$
6	3	$(6, 3)$

27.

$x$	$y$	$(x, y)$
0	$−2$	$(0, −2)$
2	$−5$	$(2, −5)$
$−2$	1	$(−2, 1)$

29.

$x$	$y$	$(x, y)$
0	2	$(0, 2)$
3	4	$(3, 1)$
6	0	$(6, 0)$

31.

$x$	$y$	$(x, y)$
0	$−2$	$(0, −2)$
10	2	$(10, 2)$
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.

ⓐ

ⓑ 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.

61.

63.

65.

67.

69.

71.

73.

75.

77.

79.

81.

83.

85.

87.

89.

91.

93.

95.

97.

99.

101.

103.

105.

107.

109.

111.

113.

115.

117.

119.

121.

123.

125.

127.

129.

131.

133.

135.

$722, $850, $978

137.

Answers will vary.

Section 4.3 Exercises

139.

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

141.

$(5, 0), (0, −5)$

143.

$(−2, 0), (0, −2)$

145.

$(−1, 0), (0, 1)$

147.

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

149.

$(0, 0)$

151.

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

153.

$(−2, 0), (0, −2)$

155.

$(5, 0), (0, −5)$

157.

$(−3, 0), (0, 3)$

159.

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

161.

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

163.

$(12, 0), (0, −4)$

165.

$(2, 0), (0, −8)$

167.

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

169.

$(4, 0), (0, −6)$

171.

$(−3, 0), (0, 1)$

173.

$(−10, 0), (0, 2)$

175.

$(0, 0)$

177.

$(0, 0)$

179.

181.

183.

185.

187.

189.

191.

193.

195.

197.

199.

201.

203.

205.

ⓐ $(0, 1000), (15, 0)$
ⓑ At $(0, 1000)$ , he has been gone 0 hours and has 1000 miles left. At $(15, 0)$ , 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.

$\frac{1}{4}$

213.

$\frac{2}{3}$

215.

$\frac{−3}{2} = - \frac{3}{2}$

217.

$- \frac{3}{4}$

219.

221.

223.

225.

227.

$\frac{2}{5}$

229.

$\frac{5}{4}$

231.

$- \frac{1}{3}$

233.

$- \frac{3}{4}$

235.

$\frac{3}{4}$

237.

$−3$

239.

$- \frac{2}{3}$

241.

$\frac{1}{4}$

243.

0

245.

undefined

247.

0

249.

undefined

251.

$\frac{5}{2}$

253.

$\frac{3}{4}$

255.

$- \frac{5}{2}$

257.

$- \frac{8}{7}$

259.

$\frac{7}{3}$

261.

$−1$

263.

265.

267.

269.

271.

273.

275.

277.

279.

ⓐ $\frac{1}{3}$ ⓑ 4 12 pitch or 4-in-12 pitch

281.

$\frac{3}{50}$ ; 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 $m = 4$ and y-intercept $(0, −2)$

291.

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

293.

slope $m = - \frac{2}{5}$ and y-intercept $(0, 3)$

295.

$−9; (0, 7)$

297.

$4; (0, −10)$

299.

$−4; (0, 8)$

301.

$- \frac{8}{3}; (0, 4)$

303.

$\frac{7}{3}; (0, −3)$

305.

307.

309.

311.

313.

315.

317.

319.

321.

horizontal line

323.

vertical line

325.

slope–intercept

327.

intercepts

329.

slope–intercept

331.

horizontal line

333.

intercepts

335.

slope–intercept

337.

ⓐ $28
ⓑ $66.10
ⓒ 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.
ⓓ

339.

ⓐ $15
ⓑ $143
ⓒ 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.
ⓓ

341.

ⓐ $750
ⓑ $2418.60
ⓒ 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.
ⓓ

343.

ⓐ $2850
ⓑ $4950
ⓒ 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.
ⓓ

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.

ⓐ For every increase of one degree Fahrenheit, the number of chirps increases by four.
ⓑ There would be $−160$ chirps when the Fahrenheit temperature is $0 °$ . (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.

$y = 4 x + 1$

389.

$y = 8 x - 6$

391.

$y = − x + 7$

393.

$y = −3 x - 1$

395.

$y = \frac{1}{5} x - 5$

397.

$y = - \frac{2}{3} x - 3$

399.

$y = 2$

401.

$y = −4 x$

403.

$y = −2 x + 4$

405.

$y = \frac{3}{4} x + 2$

407.

$y = - \frac{3}{2} x - 1$

409.

$y = 6$

411.

$y = \frac{3}{8} x - 1$

413.

$y = \frac{5}{6} x + 2$

415.

$y = - \frac{3}{5} x + 1$

417.

$y = - \frac{1}{3} x - 11$

419.

$y = 4$

421.

$y = −7$

423.

$y = - \frac{5}{2} x - 22$

425.

$y = −4 x - 11$

427.

$y = −8$

429.

$y = −4 x + 13$

431.

$y = x + 5$

433.

$y = - \frac{1}{3} x - \frac{14}{3}$

435.

$y = 7 x + 22$

437.

$y = - \frac{6}{7} x + \frac{4}{7}$

439.

$y = \frac{1}{5} x - 2$

441.

$x = 4$

443.

$x = −2$

445.

$y = 2$

447.

$y = −3$

449.

$y = 4 x$

451.

$y = \frac{1}{2} x + \frac{3}{2}$

453.

$y = 5$

455.

$y = 3 x - 1$

457.

$y = −3 x + 3$

459.

$y = 2 x - 6$

461.

$y = - \frac{2}{3} x + 5$

463.

$x = −3$

465.

$x = 4$

467.

$y = −4$

469.

$y = −1$

471.

$y = x$

473.

$y = - \frac{3}{2} x - 1$

475.

$y = - \frac{3}{4} x - \frac{1}{4}$

477.

$y = \frac{5}{4} x$

479.

$x = −5$

481.

$y = 1$

483.

$y = x + 5$

485.

$y = \frac{5}{6} x + 2$

487.

$y = - \frac{2}{3} x + 5$

489.

$y = - \frac{3}{5} x + 1$

491.

$y = 2$

493.

$y = 2 x + 4$

495.

$x = −3$

497.

$y = - \frac{1}{3} x - \frac{14}{3}$

499.

$y = \frac{3}{4} x$

501.

$y = 1.2 x + 5.2$

503.

Answers will vary.

Section 4.7 Exercises

505.

507.

509.

511.

$y < 2 x - 4$

513.

$y \leq - \frac{1}{3} x - 2$

515.

$x + y \geq 3$

517.

$x + 2 y \leq −2$

519.

$2 x - y < 4$

521.

$4 x - 3 y > 12$

523.

525.

527.

529.

531.

533.

535.

537.

539.

541.

543.

545.

547.

549.

551.

553.

ⓐ
ⓑ Answers will vary.

Review Exercises

557.

559.

561.

563.

a, b

565.

$x$	$y$	$(x, y)$
0	3	$(0, 3)$
4	1	(4, 1)
$−2$	4	$(−2, 4)$

567.

$x$	$y$	$(x, y)$
0	$3$	$(0, 3)$
2	0	$(2, 0)$
$−2$	$6$	$(−2, 6)$

569.

Answers will vary.

571.

Answers will vary.

573.

575.

577.

579.

581.

583.

585.

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

587.

$(−1, 0), (0, 1)$

589.

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

591.

$(0, 0)$

593.

595.

597.

599.

$\frac{4}{3}$

601.

$- \frac{2}{3}$

603.

605.

607.

1

609.

$- \frac{1}{2}$

611.

undefined

613.

0

615.

$−6$

617.

$\frac{5}{2}$

619.

621.

623.

$\frac{1}{10}$

625.

slope $m = - \frac{2}{3}$ and y-intercept $(0, 4)$

627.

$\frac{5}{3}; (0, −6)$

629.

$\frac{4}{5}; (0, - \frac{8}{5})$

631.

633.

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. ⓓ