4.1 points in the coordinate plane
TRANSCRIPT
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
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 2
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
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 3
4.3 Graphs of Linear Equations
Answers
1.
2.
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 4
3.
4.
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 5
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)
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 6
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)
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 7
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)
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 8
17. (0, 3) and (1.5, 0)
18. (0, -6) and (2, 0)
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 9
19. (0, -5) and (5, 0)
20. (0, 8) and (8, 0)
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 10
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.
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 11
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)
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 12
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?
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 13
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.
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 14
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)
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 15
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
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 16
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
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 17
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
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 18
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
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 19
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
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 20
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
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 21
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
Chapter 4 – Graphs of Equations and Functions Answer Key
CK-12 Algebra I Concepts 22
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