Algebra II Chapter 3 - Fort Dodge Middle School

[Pages:10]Algebra II Chapter 3

Linear Models and Systems

Refreshing Your Skills

1a) y = -26 2a) x = y +11 3

3a) y = -5

1b) a = -3

2b) y = 5 ( x - 2) + 3 3b) x = 2.083

4

1c) t ? -2.216 3c) s = 18.1+ 3.7t 4.5

3c) ratio = -2.4. It is the opposite of the slope.

1d ) y = 192 2d )b = a - 7 + 3

35

4

3.1a Linear Equations and Arithmetic Sequences

1a)

20

2a)

?u0 ??un

= =

-1 un-1

+

5

5; - 1

10

2b) 5;-1

2c) y = -1+ 5x

5 3) y = 7 + 3x

1b) -3; slope = common difference

5a) 1.7

5b) 1

5c) -4.5

5d ) 0

7a) 190 miles

7b) 82 + 54x

7c )

1c) 18; y - int = u0 1d ) y = 18 - 3x

4)

?u0 = 6 ??un = un-1 - 0.5

7d) Yes, only of you consider whole number of hours.

3.1b Linear Equations and Aritmetic

Sequences

8a)

5000

-4750, -3850, -2950, -2050, -1150, -250, 650,1550

8b) $900, profit per car

5

8c) un = -4750 + 900n

8e) $4,750; 2 cars

c = #of cars sold

-5000

p = value compared to goal

p = -4750 + 900c

8d ) vert-int: how far below goal if no cars are sold hor-int: how many cars to meet goal

10a) 0.7 cm

10b) un = 4.2 + 0.7n

10c) 34 days

Section 3.2a Revisiting Slope

1a) 3 2

1b)

-

2 3

1c) -55

2a) 3 2b) -2.8 2c) 15 3a) y = 14.3 3b) x = 6.5625

2d) 2.4

2e) - 47 32

2f)1

3c) a = -24 3d )b = -0.25

4a)

i.

y

=

-2

-

4 3

x

ii.

y

=

-2

+

3 4

x

4b)i. y = -1- 1.5x

ii. y = 3.5 + 1.5x

4c) Same Constant, -2. They have the same y-int Slopes are reciprocals with opposite signs. Lines are Perpendicular.

4d ) Same slope, -1.5 Lines are parallel. 5) Slope of l is 2.5;Slope of n is - 0.4

Section 3.2b Revisiting Slope

6a) rocket a; steepest slope 10a) Length; explain

6b) rocket c; flattest slope 6c) rocket b; slope = 2

7a) around1.47

7b) points will vary. Each battery

adds 1.47 volts. 7c) Yes. 0 batteries will

produce 0 voltage. 9a) $20,497;$17,109 9b) $849 per year

10b) 15. Each additional foot takes about 15 min.

10c) Answers will vary.

9c) in her 17th year

10d ) 32. Time to get started and finish.

Section 3.2c Revisiting Slope

13a) - 10 + 3x 14a) x = 4 17a) a > 0,b < 0 17c) a > 0,b = 0

13b) 1- 11x

13c) 28.59 + 5.4x

14b) x = -9.5

17b) a < 0,b < 0

17d ) a = 0,b < 0

Section 3.3a Fitting a Line to Data

1a) ex : y = 1+ 2 ( x - 4) 4a) 15

3

1b) ex : y = 2 + 1 ( x -1)

15

5

2a) y = -7 + 2 ( x - 5)

3

2b) y = 6 - 4( x -1)

ex : (0,5),(1,5)

5a) 3

3

ex : (-3,0),(-3,4)

2c) y = 8 + 3( x + 2) 4b) 0

5b) undefined

2d ) y = 11- 3 ( x + 4)

5 3a) u11 = 31 3b) t = -41.5

4c) y = -4

4d ) no x-int slope = 0

5c) x = 3

5d ) no y-int slope = undefined

3c) x = 1.5

same y coordinate

same x coordinate

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