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Algebra 1-2 Flexbook Q1 Solutions β Chapter 2
Chapter 2: Linear Functions
2.1 Write a Function in Slope-Intercept Form
1. π(β3) = 3; π(0) = β3; π(5) = β13
2. π(β9) = 4; π(0) = 10; π(9) = 16
3. π(π₯) = 5π₯ β 3
4. π(π₯) = β2π₯ + 5
5. π(π₯) = β7π₯ + 13
6. π(π₯) =1
3π₯ + 1
7. π(π₯) = 4.2π₯ + 19.7
8. π(π₯) = β2π₯ +5
4
9. π(π₯) = β2π₯
10. π(π₯) = βπ₯
11. sample answer: 4 times the sum of a number and 2 is 400
12. β98.8875
13. 12
3β
14. 40π/πππ
15. 121%
16. 62.52%increase
17. π€ β 6834.78
2.2 Graph a Line in Standard Form
1. π¦ = 2π₯ + 5
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2. π¦ = β3
8π₯ + 2
3. π¦ = 2π₯ β 5
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4. π¦ = β6
5π₯ β 4
5. π¦ = β3
2π₯ β 4
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6. π¦ = β1
4π₯ β 3
7. x-intercept: (6, 0) y-intercept: (0, 4)
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8. x-intercept: (β15
2, 0) y-intercept: (0, 6)
9. x-intercept: (8, 0) y-intercept: (0, β4)
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10. x-intercept: (β1, 0) y-intercept: (0, β7)
11. x-intercept: (5
2, 0) y-intercept: (0,
3
2)
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12. x-intercept: (β7, 0) y-intercept: (0,7
2)
13. x-intercept: ππππ y-intercept: (0, 3)
14. sample answer: I think converting to slope intercept form is easier because there are less steps.
15. sample answer: I would graph a vertical line at π₯ = β5. There is not y-intercept and the slope is
undefined.
2.3 Horizontal and Vertical Line Graphs
1. π¦ = 0
2. π₯ = 0
3. E: π₯ = 6
4. B: π¦ = β2
5. C: π¦ = β7
6. A: π¦ = 5
7. D: π₯ = β4
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10.
2.4 Linear Equations in Point-Slope Form
1. π¦ β 2 = β1
10(π₯ β 10)
2. π¦ β 125 = β75π₯
3. π¦ + 2 = 10(π₯ + 8)
4. π¦ β 3 = β5(π₯ + 2)
5. π¦ β 12 = β13
5(π₯ β 10)
6. π¦ β 3 = 0
7. π¦ + 3 =3
5π₯
8. π¦ β 0.5 = β6π₯
9. π¦ β 7 = β1
5π₯
10. π¦ β 5 = β12(π₯ + 2)
11. π¦ β 5 = β9
10(π₯ + 7) OR π¦ + 4 = β
9
10(π₯ β 3)
12. π¦ β 6 = βπ₯ OR π¦ = β1(π₯ β 6)
13. π¦ + 9 = 3(π₯ + 2)
14. π¦ β 32 = β9
5π₯
15. π¦ β 20 =1
40(π₯ β 100) OR π¦ β 25 =
1
40(π₯ β 300) The length of the spring before it is stretched is
17.5 cm.
16. π¦ β 400 = β35
2π₯ OR π¦ β 50 = β
35
2(π₯ β 20) The depth of the submarine five minutes after it
started surfacing would be 312.5 ft.
2.5 Writing and Comparing Functions
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9.
10.
11. π(π‘) = 1100 β 30π‘ OR π(π‘) = β30π‘ + 1100
12. π = β30
13. π(π‘) = 2000 β 20π‘ OR π(π‘) = β20π‘ + 2000
14. slope: (#11) π = β30 (#12) π = β20; The distanced traveled each day is larger for the migrating
monarch so it flies at a faster rate.
y-intercepts: (#11) (0, 1100) (#12) (0, 2000); The y-intercept in this scenario represents the total
distance the butterfly must travel, or the amount of miles left to travel on day zero.
x-intercepts: (#11) (362
3, 0) (#12) (100, 0); The x-intercept in this scenario represents the amount of
time it takes to travel the total migrating distance.
Domain: (#11) 0 β€ π‘ β€ 362
3 (#12) 0 β€ π‘ β€ 100
Range: (#11) 0 β€ π(π‘) β€ 1100 (#12) 0 β€ π(π‘) β€ 2000
15. π(π₯) = 1.5 + 3000
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16. π = 1.5
17. The writer needs to sell 4667 books.
2.6 Applications of Linear Models
1. π¦ = 350π₯ + 1500; x= #of months y=amount paid
Constraints: The number of months (x) would include integers greater than or equal to zero until the car
is paid off. The amount paid would start at $1500 then add an amount of $350 per month until the car
is paid off.
Domain: {0, 1, 2, 3, β¦ } until paid off
Range: {1500, 1850, 2150, β¦ } until paid off
2. π¦ =1
2π₯ +
17
2; x=# of weeks; y= height of the plant (in)
Constraints: The number of weeks could be 0 weeks or greater, including a fraction of a week. The
height could be greater than or equal to 8.5 inches.
Domain: π₯ β₯ 0
Range: π¦ β₯ 8.5
The height of the rose was 8.5 inches when Anne planted it.
3. π¦ =1
40π₯ + 1; x=weight (lbs.) y=length of spring (m)
Constraints: The weight could be 0 lbs. or greater, including fractions of a pound; the length could be
greater than or equal to 1 m since that is the length of the spring with no weight attached. There would
be a limit to both when the weight would cause the spring to hit the ground.
Domain: π₯ β₯ 0
Range: π¦ β₯ 1
The spring would be 4.5 meters long when Amardeep hangs from it.
4. π¦ =1
2π₯ + 215; x=weight (lbs.) y=distance stretched (ft.)
Constraints: The weight could be 0 lbs. or greater, including fractions of a pound; the length would be
greater than or equal to 215 ft. which is the length of the cord before it is stretched (within the values
that represent a linear function).
Domain: π₯ β₯ 0
Range: π¦ β₯ 215
The expected length of the cord would be 290 ft. for a weight of 150 lbs.
5. π¦ β 20 =1
40(π₯ β 100); x=weight (g) y=length (cm)
Constraints: The weight could be 0 g or greater, including fractions of a gram; the length would be
greater than or equal to 17.5 cm which is the length of the cord before it is stretched.
Domain: π₯ β₯ 0
Range: π¦ β₯ 17.5
6. π¦ β 400 = β35
2π₯; x=time (mins) y=depth (ft)
Constraints: The time would be between 0 and 22.86 minutes (the time it takes to surface) and the
depth would be any measure between 400 and 0 feet.
Domain: [0, 22.86]
Range: [0, 400]
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7. π¦ β 2500 = 6(π₯ β 200); x= # of shades sold y=amount $$ made
Constraints: It would be possible to sell zero shades and any whole number greater than zero so the
positive integers are appropriate; the amount made each month would be a minimum of $1300 plus $6
for each shade thereafter.
Domain: positive integers greater than or equal to zero
Range: {1300, 1306, 1312, β¦ }
8. You can only buy one pound of corn.
9. 165 baked fish dinners were sold.
10. Andrew needs to work 36 hours at his $6/hour job to make $366.
11. She needs to invest $2142.86 or less in the account with 7% interest.
12. π¦ = 6π₯ β 16
13. π = β19
14. The graph of π₯ = 1.5 is a vertical line at π₯ = 1.5 where the value of x is always 1.5 for any value of y.
15. No it is not a solution.
16. sample answer: (-4, -2); Quadrant III is (-x,-y)
17. π = 0
18.
2.7 Rates of Change
1. Slope is the rate of change when considering a linear equation or function because the rate of change
is constant.
2. traffic light = B; mending tire = E; hills in order of most steep to least steep: A, F, C, D
3. 512
3/βπ OR 155ππ/3βππ
4. $24/π€πππ
5. sample answer: An elevator moves at 10 ft/sec.
6. x-intercept: (10
3, 0); y-intercept: (0, β2)
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7.
8. sample answer:
9. Although this can be graphed as a linear function, keep in mind the constraints of dimes and quarters.
You canβt have a negative amount of either and you canβt have a portion of either (i.e. 37.5 dimes). In
reality, the graph should be a set of discrete points rather than a continuous linear function.
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10. domain: {β2, β1, 0, 1, 2}; range: {2, 1, 0, 1, 2}
11. π¦ = 6.75
12. 3π₯ + 1 = 2π₯ β 35
β1 β 1 subtraction property of equality
3π₯ = 2π₯ β 36 substitution property of equality (simplify)
β2π₯ β 2π₯ subtraction property of equality
π₯ = β36 substitution property of equality (simplify)
13. π = 3
Quick Quiz
1. x-intercept: (25
3, 0); y-intercept: (0,
35
36)
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2. π = β1
13
3.
4.
5. sample answer: Membership has been steadily increasing over the last 10 years. The increase in
membership was the same from year to year for the first two years.
2.8 Linear and Non-Linear Function Distinction
1. non-linear
2. linear
3. linear
4. linear
5. non-linear
6. linear
7. linear
8. non-linear
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9. linear
10. non-linear
11.
12.
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19.
20.
2.9 Comparing Function Models
2.29 linear
2.30 non-linear
2.31 linear
2.32 not quadratic
2.33 quadratic
2.34 not quadratic
2.35 not exponential
2.36 exponential
2.37 exponential
2.38 exponential
2.39 linear
2.40 quadratic