O R C U T T A C A D E M Y H I G H S C H O O L

C O R E C O N N E C T I O N S A L G E B R A 1

Chapter 2 Linear Functions

2.1.1 CW Answers 2-1. See below:

a) Figure 4 has 16 tiles; Figure 0 has four horizontal tiles.

b) Grows by 3 tiles. One tile is being stacked on the left, and two tiles are being stacked on the right.

c) The left tower has 100 tiles, the right tower has 200 tiles, and there are 4 horizontal tiles between the towers. Figure 100 has 304 tiles.

d) y = 3x + 4

2-2. Figure 0 has 3 tiles. Figure 4 has 11 tiles. Figure 100 has 203 tiles. y = 2x + 3. See "Suggested Lesson Activity" for a diagram of shaded tiles.

2-3. See below:

a) See answers in bold in the table below.

Figure # (x) 0 1 2 3 4

# of Tiles (y) 1 4 7 10 13

b) Growth 3 tiles. Starting value 1 tile.

c) The growth is found by how much the number of tiles increases from one figure to the next. The starting value is at Figure 0.

d) The growth is the multiplier (coefficient) of x and the starting value is the constant added to it.

2.1.1 CW Answers 2-4. You would need to know the number of tiles in Figure 0 (or any other single figure) and the number of tiles that are added for each figure.

2-5. See below:

a) Figure 0 has 1 tile, and Figure 4 has 17 tiles.

b) y = 4x + 1

c) See answers in bold in the table below.

Figure # (x) 0 1 2 3 4

# of Tiles (y) 1 5 9 13 17

d) Both patterns would have 1 tile in Figure 0. Pattern C grows by 3, while Pattern D grows by 4.

e) The similarities can be seen at the “+1” in both equations; the differences can be seen at the multiplier in the equations.

f) The similarities can be seen at Figure 0 in the table; the differences can be seen by how much the # of tiles increases each time in the table.

2.1.1 Answers 2-6. y = 7x + 5

2-7. See below:

a) 5

b) −1

c) 132

d) −2

2-8. See below:

a) 2

b) −4

c) −5, −2, 0, 2, 4

d) −2

e) 13

2-9. (a) and (b) are functions because each only has one output for each input.

a: D: all real numbers, R: 1 ≤ y ≤ 3; b: D: all real numbers, R: y ≥ 0;

c: D: x ≥ −2, R: all real numbers

2-10. All graphs have lines of symmetry. Graph (a) has multiple vertical lines of symmetry, one at each maximum and minimum; graph (b) has one line of symmetry at x = 1; graph (c) has one line of symmetry at y = 1.

2.1.2 Answers 2-19. Possible response: It is a parabola because it has an x2-term. (This conclusion is acceptable at this point.) Solution graph shown at right.

2-20. See below:

a) −10

b) −3

c) −3

d) −22

3

2-21. Answers vary.

2-22. y = 3x

2-23. No solution; you cannot divide by zero.

2-24. m = 1

3

2.1.3 Answers 2-31. 𝑓(𝑥) = 4𝑥 + 4

2-32. See below:

a) Line a: 𝑦 = 2𝑥 − 2, Line b: 𝑦 = 2𝑥 + 3

b) It would lie between lines a and b, because its y-intercept is at (0, 1).

c) It would travel downward but would have the same y-intercept as the line from part (b).

2-33. 𝑦 = 𝑥 − 4

2-34. Answers vary.

2-35. x ≠ −5 because the denominator cannot be 0.

2.1.4 Answers

2-41. See below.

a) m = 1

2

b) (0, −4).

See graph.

2-42. See below.

a) m = –2

b) m = 0.5

c) undefined

d) m = 0

2-43. No; when x = 12, y = 102, so it would have 102 tiles.

2-44. See below.

a) m = 5

3 , b = (0, –4)

b) m = − 4

7, b = (0, 3)

c) m = 0, b = (0, –5)

2-45. See below.

a) −18

b) −4

c) undefined

d) −5

2.2.1 Answers 2-48. See below:

a) 4

b) 16

c) y = 4x + 16

d) It would get steeper.

2-49. See below:

a) −4

3

b) (0, −5)

c) y = − 4

3 x − 5

2-50. See below:

a) x = 12

b) w = 0

c) x = −8

d) no solution

2-51. y = −4x − 3

2-52. Graphs (a) and (b) have a domain of all numbers, while graphs (a) and (c) have a range of all numbers. Graphs (a) and (b) are functions.

2.2.2 Answers 2-59. y = 2x + 3

2-60. Find solutions in the diamonds below:

2-61. See below:

a) The dependent variable is distance in meters and the independent variable is time in seconds.

b) See graph at right. Mark won the race, finishing in 5 seconds.

c) Barbara: y = 3

2x + 3, Mark: y = 4x

d) 5 meters every 2 seconds, or 5

2 meters per second.

e) 2 seconds after the start of the race, when each is 6 meters from the starting line.

2.2.2 Answers 2-62. x-intercept: (2, 0), y-intercept: (0, –10)

2-63. m = 3

2-64.

2-65. See below:

a) y = −2x + 1

b) x: (0.5, 0), y: (0, 1)

2-66. See below:

a) 1

b) 0

c) 2

d) 7

2-67. See below:

a) G = 5, Fig 0 = 3

b) G = –2, Fig 0 = 3

c) G = 3, Fig 0 = –14

d) G = –5, Fig 0 = 3

2.2.3 Answers 2-70. See below: a) (4, 0) and (0, –2)

b) (8, 0) and (0, 4) 2-73. See answers in bold in the table below. y = –5x + 3

2-71. See below:

a) –1

b) –1

2

c)3

2

d) –1

5

e) The line travels downward from left to right, so m = –1.

2-72. See below:

a) 23865

b) –371

8

c) –51

8

d) –61

3

2-74. See below:

a) 4

b) 3

c) 1

d) 2

2.3.1 Answers

2-82. See below:

a) y = 1.5x + 0.5

b) Answers vary, but solutions should lie on y = 1.5x + 0.5. Possible points: (0, 0.5), (1, 2), (10, 15.5)

2-83. Find solutions in bold in the diamonds below:

2-84. See below:

a) (3.5, 0) and (0, –2.33)

b) y = 13

3 ≈ 4.33

2-85. See below:

a) 3, (0, 5)

b)5

4, (0, 0)

c) 0, (0, 3)

d) 4, (0, 7)

2-86.

2.3.2 Answers

2-90. See below:

a) The slope represents the change in height of a candle per minute, m = 0 cm per minute.

b) The slope represents the gallons per month of water being removed from a storage tank, m = −900 gallons per month.

2-91. y = −3x + 25

2-92. See below:

a) −8

b) 1

c) −2

d) 17

e) −45

f) 125

2-93. A = 50w + 100, A = (50)(52) + 100 = 2700

2-94. See below:

See answers in bold in the table below.

a)

b)−3 𝑐𝑚

2 𝑑𝑎𝑦 or −1.5 cm/day

c) y = −3

2x + 30