4.1 Points in the Coordinate Plane

Chapter 4 – Graphs of Equations and Functions Answer Key

CK-12 Algebra I Concepts 1

4.1 Points in the Coordinate Plane

Answers

1. a. (5, 6) b. (-5, 5) c. (-2, 3) d. (-2, -2) e. (3, -4) f. (2, -6)

2. (-2, 2)

3.- 6.

7. I

8. III

9. II

10. IV



4.2 Graphs in the Coordinate Plane

Answers

1. I and II

2. I and III

3. I, II, and III

4. I and IV

5. III and IV

6. II

7. Point D should be located at (-4, 3)

8. Quadrant III

9. (1, 4)

10. (4, 8)

11. (5, 2)

12. (0, 0) or ‘the origin’

13. a. 𝑦 = 3𝑥

b.

c.

𝑦 (Starburst) 0 3 6 9 12 15 𝑥 (M&M) 0 1 2 3 4 5



4.3 Graphs of Linear Equations

Answers

1.

2.



3.

4.



5. (The equation for a, b, c, d is 𝑦 = 0.7(𝑥 − 5) a.

b. c. 31.5 euro d. $55 e. $75

6. ≈ 9𝑙𝑏𝑠 7. ≈ 20𝑙𝑏𝑠 8. ≈ 5.5𝑘𝑔 9. ≈ 7.5𝑘𝑔 10. 5 weights (the graph indicates that 8𝑘𝑔 < 18𝑙𝑏) 11. 2 weights 12. 3 more weights (the graph indicates that 9𝑘𝑔 ≈ 20𝑙𝑏𝑠)



4.4 Horizontal and Vertical Line Graphs

Answers

1. a. 𝑦 = 5 b. 𝑦 = −2 c. 𝑦 = −5 d. 𝑥 = −4 e. 𝑥 = 6

2. (6, 5) 3. (-4, 5) 4. (-4, -7) 5. (0, -2) 6. (6, 0) 7. (-7, -7) 8. (6, 3) 9. (2, 5) 10. (1, -2)



4.5 Intercepts and the Cover-Up Method

Answers

1. (0, -6) and (2, 0) 2. (0, 4) and (2, 0) 3. (0, -21) and (1.5, 0) 4. (0, 7) and (7/3, 0) 5. (0, -4) and (1.6, 0) 6. (0, 2.2) and (-2, 0) 7. (0, 7) and (-18 2/3, 0) 8. (0, 5/9) and (1 17/18, 0) 9. (0, -2.5) and (3, 0) 10. (0, 5/4) and (-5/3, 0) 11. (0, -11/7) and (-11/2, 0) 12. (0, 2.5) and (5, 0) 13. (0, -9.23) and (12/5, 0) 14. (0, -2) and (5, 0) 15. (0, 1/5) and (2/3, 0) 16. (0, -3/10) and (4/15, 0)



17. (0, 3) and (1.5, 0)

18. (0, -6) and (2, 0)



19. (0, -5) and (5, 0)

20. (0, 8) and (8, 0)



21.

22.

23. The equation needs to be distributed first.

24. Answers will vary but should include two equations that are not in standard form 𝑎𝑥 +

𝑏𝑦 = 𝑐, where a and b are constants.



4.6 Slope

Answers

1. 𝑚 = =>?>@>?

= =>@

2. 𝑚 = >@>AA>B>B

= ACC= D

B

3. 𝑚 = >@>E

B>(>F)= − AH

@

4. 𝑚 = =>AA

>@>(>@)= − H

?= 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑

5. 𝑚 = E>(>E)

E>(>E)= 1

6. 𝑚 = @>=

B>(>F)= − F

@

7. 𝑚 = B>(B.@)

F.@>D= >.@

>@.@= A

AA

8.

a. 𝑚 = AFH= 3

b. 𝑚 = BC= A

F

9.

c. 𝑚 = −AFC= −2

d. 𝑚 = CC= 1

10.

e. 𝑚 = D?= 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑

f. 𝑚 = BE= A

B

11. Answers will vary, below are examples

a. (2, 4) b. (3, 2) c. (2, -1) d. (2, 2) e. (9, 0) f. (4, 2)



4.7 Rates of Change

Answers

1. Riding uphill 2. Stopped at light 3. Riding uphill 4. Riding downhill 5. Stopped to fix tire 6. Riding uphill 7. 𝑚 ≈ ?.@

@𝑜𝑟 A

A?

8. 𝑚 = 0 9. 𝑚 ≈ .=

=𝑜𝑟 A

A?

10. 𝑚 ≈ A

B

11. 𝑚 = 0 12. 𝑚 ≈ ?.@

@𝑜𝑟 A

A?



4.8 Graphs Using Slope-Intercept Form

Answers

1. 𝑚 = 2, 𝑏 = 5 2. 𝑚 = −0.2, 𝑏 = 7 3. 𝑚 = 1, 𝑏 = 0 4. 𝑚 = 0, 𝑏 = 3.75 5.

a. 𝑚 = −2 b. 𝑚 = −H

B

c. 𝑚 = ?H= 0

d. 𝑚 = F@

e. 𝑚 = −FD= −A

H

f. 𝑚 = −FH= −A

F

g. 𝑚 = HA= 4

6.

a. 𝑚 = −FB, 𝑏 ≈ 1.5

b. 𝑚 = 3, 𝑏 = 1 c. 𝑚 = A

F, 𝑏 = −2

d. 𝑚 = −1, 𝑏 = 0 e. 𝑚 = 0, 𝑏 = 3 f. 𝑚 = −A

@, 𝑏 = −1

7. – 10.



11. Lines b and e are parallel, both have 𝑚 = −A@= −0.2

12. 𝑏 = −7 13. 𝑏 = 7 14.

a. 𝑦 = AF𝑥 + 5

b. 𝑦 = AF𝑥 + 1

15. Answers may vary, most likely correct answer is (1, 4.5)



4.9 Graphs of Linear Models of Direct Variation

Answers

1.-4.

5. a. 𝑦 = 0.35𝑥 so he can play for 57 minutes b. 𝑦 = 65𝑥 so he shoots 975 aliens c. He will not beat it in 15 minutes, he will in 20 minutes

6.

a. 12 minutes b. 15 minutes c. 60 minutes d. 20 minutes

7.

a. Noon b. 2 pm c. 5 @

=𝑜𝑟5.71 gallons

d. 10 gallons

8. a. $51,853.45 b. 115.71 acres



9. a. 𝑘 = 1.2 b. 𝐹 = 8.4N c. 𝑥 = 19 A

C𝑐𝑚

10. 6:20 pm

11.

a. Not a direct variation b. $200 c. $180 d. $175



4.10 Graphs of Linear Functions

Answers

1. 76.44 m/s 2.

a. 𝑣 = 20 − (0.16𝑚) b. 125 minutes

3. 𝑓(−3) = 9, 𝑓(0) = 3, 𝑓(𝑧) = −2𝑧 + 3, 𝑓(𝑥 + 3) = −2𝑥 − 3, 𝑓(2𝑛) = −4𝑛 + 3, 𝑓(3𝑦 + 8) =

−6𝑦 − 13, 𝑓 UVFW = −𝑞 + 3

4. 𝑓(−3) = 1.1, 𝑓(0) = 3.2, 𝑓(𝑧) = 0.7𝑧 + 3.2, 𝑓(𝑥 + 3) = 0.7𝑥 + 5.3, 𝑓(2𝑛) = 1.4𝑛 + 3.2,

𝑓(3𝑦 + 8) = 2.1𝑦 + 8.8, 𝑓 UVFW = 0.35𝑞 + 3.2

5. 𝑓(−3) = F@

AA, 𝑓(0) = A?

AA, 𝑓(𝑧) = @(F>Y)

AA= A?>@Y

AA, 𝑓(𝑥 + 3) = >@(Z[A)

AA, 𝑓(2𝑛) = @(F>F\)

AA= A?(A>\)

AA,

𝑓(3𝑦 + 8) = >A@]>B?AA

, 𝑓 UVFW =

A?>U^_WV

AA

6. Function 7. Not a function 8. Not a function 9. Function 10.

a. 𝑡 = 8𝑥 + 100 b. 180 minutes c. 316 minutes d. 20 pounds

11. 45 12. -1 13. 9.75, 6.5, 3.25



4.11 Problem Solving with Linear Graphs

Answers

1.

In blue: , in green: , in red:

a. ≈ $670 b. ≈ $20 (the “old membership” costs apx $690/year) c. The costs are the same at 10 months

y = 39x + 200 y = 49x +100 y = 49x +100 x =12



2.

In blue: 𝑦 = −A

B𝑥 + 5 F

B

a. apx 5.6 inches b. apx 15 ½ mins c. It would take 36 stubs (assuming no partial stubs, or about 35 ½ allowing

partials)

3.

In black: 𝑦 = B

F𝑥 + 2

a. 2mm b. 200 = B

F𝑥 + 2 ∶ AEDc

_= 𝑥 ∶ 𝑥 = 132𝑑𝑖𝑝𝑠



4. Each page is apx AHH?

𝑖𝑛𝑐ℎ𝑒𝑠

5.

In blue: 𝑦 = 0.45𝑥 : In red: 𝑦 = 25

a. They need to sell 56 glasses b. $0.70

6. 6 ¼ cups

7.

In blue: 𝑦 = 350𝑥 + 1500 : In red: 𝑥 = 12

a. $5700 b. 20 months c. $6500



8.

The rose was 7” tall. In black: 𝑦 = F

B𝑥 + 7

9. 𝑦 = A

H?𝑥 + 1 : 4.5 inches

10.

In blue: 𝑦 = AH?𝑥 + 17.5 : In red: y=35

a. 17.5 cm b. 700 g



11.

In blue: 𝑦 = −B@

F𝑥 + 400 : in red 𝑥 = 5

a. 310 ft b. apx 3 mins

12.

a. 15 mins b. 25 mins to fully charge

13.

a. H@=@= 60%

b. 2:21 c. 15 mins

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4.1 Points in the Coordinate Plane