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AK-1North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
UNIT 2 • LINEAR FUNCTIONS
Answer KeyLesson 2.1: Proving Average Rate of Change (F–LE.1a•)
Warm-Up 2.11. BoatAwillbeworth$5,145after3years.2. BoatBwillbeworth$6,144after3years.3. BoatBwillbeworthmorethanBoatAafter3years.
Practice 2.1 A: Proving Average Rate of Change1. –0.92. –323. 46.744. –15.185. 1.8
6. 0.087. 0.088. 7.59. 13.65
10. 14.77
Practice 2.1 B: Proving Average Rate of Change1. –0.022. 203. 30.724. –5.475. 2.54
6. 0.137. 0.138. 149. 24.40
10. 26.98
Lesson 2.2: Recognizing Average Rate of Change (F–LE.1b•, F–LE.1c•)
Warm-Up 2.21. Therateofchangefrom1900to2000was2.03millionper
year.Therateofchangefrom2000to2010was3.5millionperyear.Therateofchangefor1900to2000waslessthantherateofchangefor2000to2010.
2. Highestrateofchange:Either1950to1960or1990to2000couldbedescribedasthe10-yearperiodwiththehighestrateofchange,becausetheyseemtohaveidenticalrates.Lowestrateofchange:1930to1940.Calculatetherateofchangeforeach10-yearperiod.
3. Answerswillvary.Sampleanswer:Thepopulationin2020couldreach348,000,000iftherateofchangecontinuesat3.5millionperyear.
Practice 2.2 A: Recognizing Average Rate of Change1. ≈0.001gallonsperfoot2. ≈0.001gallonsperfoot3. ≈0.8EurosperU.S.dollar4. ≈0.8EurosperU.S.dollar5. Yes,apredictionispossible.Sampleprediction:Therate
ofchangewouldbethesameastherateofchangeinquestions3and4becausethefunctionislinear.
6. ≈25visitorsperyear7. ≈29visitorsperyear8. ≈–271peopleperyear9. ≈–167peopleperyear
10. Therateofchangefortheinterval[2,9]issteeperthantheintervalfrom[14,20].Thepopulationisdecreasingatafasterratefortheinterval[2,9]thanfor[14,20].
Practice 2.2 B: Recognizing Average Rate of Change1. ≈0.06gallonsperdoor2. ≈0.06gallonsperdoor3. ≈0.97AustraliandollarsperU.S.dollar4. ≈0.97AustraliandollarsperU.S.dollar5. Yes,apredictionispossible.Sampleprediction:Therate
ofchangewouldbethesameastherateofchangeinquestions3and4becausethefunctionislinear.
6. ≈92campersperyear7. ≈150campersperyear8. ≈–160peopleperyear9. ≈–65peopleperyear
10. Therateofchangefortheinterval[1,6]issteeperthantheinterval[10,13].Thepopulationisdecreasingatafasterratefortheinterval[1,6]thanfor[10,13].
Lesson 2.4: Working with Parallel and Perpendicular Lines (G–GPE.5)
Warm-Up 2.41. Answersmayvary.Eachequationshouldhaveaslopeof
–5.Onepossibleanswerisy=–5x+2.y-interceptsmustbedifferentforlinestobeparallelandnotcoinciding.
2. Answersmayvary.Eachequationshouldhaveaslopeof–5.Onepossibleanswerisy=–5x+7.y-interceptsmustbedifferentforlinestobeparallelandnotcoinciding.
Practice 2.4 A: Working with Parallel and Perpendicular Lines
1. y=–2x+7
2. y x4
3
2
3=−
−
3. y x1
42= −
4. y = –x–15. 2 1.4 units≈
6. y x3
47=− +
7. y=–5x–34
8. y x1
510= +
9. y x4
32= −
10. TheshortestdistanceisthelinethatisperpendicularfromthetrainstationtoUnionStreet.Thisdistanceisapproximately647yards.
AK-2North Carolina Math 1 Teacher Resource/Student Workbook Answer Key
© Walch Education
Practice 2.4 B: Working with Parallel and Perpendicular Lines
1. y=3x–8
2. y x1
4=−
3. y x1
37= +
4. y=–2x+2
5.80
25or 1.79 units≈
6. y x1
2
7
2= −
7. y x1
3
7
3= +
8. y=–3x–169. y=–2x–3
10. Theshortestdistanceisthelinethatisperpendicular
fromthegrocerystoretoMapleStreet.Thisdistanceis81
102.85 units≈ or285yards.
Lesson 2.5: Interpreting Parameters (F–LE.5•)
Warm-Up 2.51. f(x)=2x+52. They-interceptis5.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
(0, 5)
(1, 7)
3. themembershipfee4. thecosttorenteachgame
Practice 2.5 A: Interpreting Parameters1. slope=7;y-intercept=52. growthfactor=2;verticalshift=33. slope=–2;y-intercept=104. startingquantity=2;growthfactor=35. startingquantity=3;growthfactor=2;verticalshift=56. f(x)=2x+10;slope=2;y-intercept=10
7. slope=1.25;y-intercept=58. Maxpicks18applesperminuteandstartedwith15apples
inhisbag.9. Youhad10antsinthecolonytostartwith,andthe
numberofantsdoublesevery36hours.10. f(x)=150(2x)+200;growthfactor=2;
startingamount=$150;verticalshift=$200
Practice 2.5 B: Interpreting Parameters1. slope=3;y-intercept=122. growthfactor=4;verticalshift=–83. slope=–6;y-intercept=134. growthfactor=2;startingamount=55. growthfactor=4;startingamount=2;verticalshift=96. f(x) =300(3x)+100;growthfactor=3;starting
amount=$300;verticalshift=$1007. slope=2.5;y-intercept=78. slope=3.75;y-intercept=129. Kendallpicks35strawberriesperminuteandstartedwith
20strawberriesinhisbasket.10. Therewere25antstostartwithandthepopulationgrows
atarateof3antsevery4days.
Lesson 2.6: Graphing the Set of All Solutions (A–REI.10)
Warm-Up 2.61. $52. $93. Theslopeofthegraphis2.ThegraphshowsthatMallory
canreceive$2onthey-axisforevery1dayonthex-axis.
Practice 2.6 A: Graphing the Set of All Solutions1.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
AK-3North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
2.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6-5-4-3-2-1
123456789
10
3.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6-5-4-3-2-1
123456789
10
4.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6-5-4-3-2-1
123456789
10
5. {(0,1);(–2,4);(–3,8)}6. {(0,7);(8,6);(–8,8)}
7. Theprofitinyear7shouldbeabout$929.34.
0 1 2 3 4 5 6 7 8
100
200
300
400
500
600
700
800
900
1000
Years
Pro�
t in
dolla
rs
8. y=2x;for4batchesofcookies,Katyaneeds8eggs.
0 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
Batches of cookies
Eggs
nee
ded
9.1
435.50y x= + ;at12months,thepricewillbe$38.50.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
32
33
34
35
36
37
38
39
40
Months
Pric
e pe
r sha
re
AK-4North Carolina Math 1 Teacher Resource/Student Workbook Answer Key
© Walch Education
10. Youwouldhavetopay$22.50for7.5gallonsofgas.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5
10
15
20
25
30
35
40
45
50
55
Gallons of gas
Am
ount
pai
d
Practice 2.6 B: Graphing the Set of All Solutions1.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6-5-4-3-2-1
123456789
10
2.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6-5-4-3-2-1
123456789
10
3.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6-5-4-3-2-1
123456789
10
4.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6-5-4-3-2-1
123456789
10
5. {(0,2);(2,5);(4,8)}6. {(–2,9);(–1,3);(0,1)}7. Thepainterwillhave35gallonsremainingafter6hours.
0 1 2 3 4 5 6 7 85
10
15
20
25
30
35
40
45
50
55
60
65
70
Hours
Gal
lons
of p
aint
AK-5North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
8. Therewereabout1.6gramsofbacteriaafter60hours.
0 10 20 30 40 50 60 70 80 90 100 110 1202
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
Hours
Gra
ms
9. Enricowouldhavetoride49milesonthefifthday.
0 1 2 3 4
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
Days
Mile
s
10. Itwilltakejustmorethan24monthsforMr.Samuelson’ssavingstoexceedhiscosts.
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42
500
1000
1500
2000
2500
3000
3500
4000
Months
Savi
ngs
in d
olla
rsLesson 2.7: Sequences As Functions (F–IF.3)
Warm-Up 2.71. Saturday,May72. Friday,May133. Thursday,May19
Practice 2.7 A: Sequences As Functions1. 282. 233.
0 1 2 3 4 5 6 7
-5-4-3-2-1
123456789
1011121314151617181920an
n
AK-6North Carolina Math 1 Teacher Resource/Student Workbook Answer Key
© Walch Education
4.
0 1 2 3 4 5 6 7-2-1
123456789
1011121314151617181920212223242526272829303132
an
n
5. 756. 1047. a
5=162
0 1 2 3 4 5 6 7
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500an
n
8. a5=45,a
6=53
0 1 2 3 4 5 6 72468
1012141618202224262830323436384042444648505254an
n
9. 2:01p.m.10. Thefifthwaterstationwillbeatthe19-milemark.
Practice 2.7 B: Sequences As Functions1. 322. 22
0 1 2 3 4 5 6 7123456789
10111213141516171819202122232425an
n
AK-7North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
3. 53
0 1 2 3 4 5 6 72468
101214161820222426283032343638404244464850525456586062646668an
n
4. 395. 326. 2977. a
5=21,a
6=25
0 1 2 3 4 5 6 71
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26an
n
8. a5=32,a
6=64
0 1 2 3 4 5 6 7 8 948
12162024283236404448525660646872768084889296
100104108112116120124128an
n
9. 5:53a.m.10. Thelargestcontainerholds32gallons;thesmallest
containerholds2gallons.
Lesson 2.8: Building Functions from Context (F–BF.1a•)
Warm-Up 2.81. c=4p;$42. d=55t;330miles
3. t=4s;120students4. p=12h;36pages
Practice 2.8 A: Building Functions from Context1. f(x) =19+12x2. f(x)=–5x+303. f(x)=132–22x4. f(x)=12•(5)x –1
5. f(x)=32•(0.5)x
6. f(x)=2+x7. f(x)=3x –1
8. f(x)=4x –1
9. f(x) = 150+25(x–1)10. f(x)=10,000(1.10)x
Practice 2.8 B: Building Functions from Context1. f(x)=15x2. f(x)=–18x+2603. f(x)=7+9x4. f(x)=6•4x –1
5. f(x)=60•(0.9)x
6. f(x)=x7. f(x)=4x–38. f(x)=2xorf(x)=2•2x –1
9. f(x) =10+0.25x10. f(x)=15,000•(0.80)x
AK-8North Carolina Math 1 Teacher Resource/Student Workbook Answer Key
© Walch Education
Lesson 2.12: Solving Problems Given Functions Fitted to Data (S–ID.6a•)
Warm-Up 2.121.
0 2 4 6 8 10 12 14 16 18
2
4
6
8
10
12
14
16
18
Cost
in d
olla
rs ($
)
Number of goods
2.
Practice 2.12 A: Solving Problems Given Functions Fitted to Data
1.
Trac
k le
ngth
in m
iles
Time in minutes
2. Thescatterplotcouldbeestimatedusingastraightline.Alinearfunctionisabetterfitforthedata.
3.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
y = 3.3x
y = 2.3x
Trac
k le
ngth
in m
iles
Time in minutes
y=3.3xisabetterfitforthedatabecauseitmorecloselyfollowsthetrendinthepoints.
4. 0.545minutes5. 1.98miles
AK-9North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
6.
0 1 2 3 4 5 6 7 8
2000
4000
6000
8000
1 104
1.2 104
1.4 104
1.6 104
1.8 104
2 104Va
lue
of c
ar, i
n do
llars
($)
Year
7. Anexponentialfunction;thegraphisacurve,andtheverticaldistancebetweenthepointsisdecreasingasthehorizontaldistanceremainsconstant.
8. Thegraphofy=19,000(1.10)xisnotagoodestimateforthedatabecauseitdoesn’tapproachanyofthedatapointsonthescatterplot.However,thegraphofy=19,000(0.90)xisagoodestimatebecauseitgoesthroughorcloselyapproachesallofthedatapoints.
0 1 2 3 4 5 6 7 82000
4000
6000
8000
1 104
1.2 104
1.4 104
1.6 104
1.8 104
2 104
2.2 104
2.4 104
2.6 104
2.8 104
3 104
y = 19, 000 • (1.10)x
y = 19, 000 • (0.90)x
Valu
e of
car
, in
dolla
rs ($
)
Year
9. 7.1years,becauselookingatthetrendinthegraph,thecurvefallsthrough$9,000atabout7.1years.
0 1 2 3 4 5 6 7 82000
4000
6000
8000
1 104
1.2 104
1.4 104
1.6 104
1.8 104
2 104
2.2 104
2.4 104
2.6 104
2.8 104
3 104
Valu
e of
car
, in
dolla
rs ($
)
Year
10. approximately$5,366
Practice 2.12 B: Solving Problems Given Functions Fitted to Data
1.
0 1 2 3 4 5 6 720
40
60
80
100
120
140
160
180
200
220
240
New
vis
itors
Day
2. Anexponentialfunction;thegraphisacurve,andtheverticaldistancebetweenthepointsisincreasingasthehorizontaldistanceremainsconstant.
AK-10North Carolina Math 1 Teacher Resource/Student Workbook Answer Key
© Walch Education
3.
0 1 2 3 4 5 6 720
40
60
80
100
120
140
160
180
200
220
240
y = 4x y = 3x
New
vis
itors
Day
Thefunctiony=3xisabetterfitbecauseitmorecloselyfollowsthedatatrend.
4. onday65. approximately2,187visitors6.
0 1 2 3 4 5
10
20
30
40
50
60
70
80
90
100
Sand
wic
hes
rem
aini
ng
Hours open
7. Thescatterplotcouldbeestimatedusingastraightline.Alinearfunctionisabetterfitforthedata.
8.
0 1 2 3 4 5 6
10
20
30
40
50
60
70
80
90
100
y = -3.8x + 92
y = -5.8x + 99
Sand
wic
hes
rem
aini
ng
Hours open
y=–5.8x+99,becausethecurvefollowsthetrendinthedata.
9. approximately98sandwiches10. approximately17hours
Lesson 2.13: Analyzing Residuals (S–ID.6b•)
Warm-Up 2.131.
0 1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
7
8
9
2. Thedistanceistheabsolutevalueofthedifferencebetweenthetwoy-values:|6–4|=2.
AK-11North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
3.
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
1
2
3
4
Practice 2.13 A: Analyzing Residuals1.
0 5 10 15 20 25 30 35 40 45 50 55
10
20
30
40
50
60
70
80
90
100
110
Dee
r
Acres
2.
0 5 10 15 20 25 30 35 40 45 50 55 60
10
20
30
40
50
60
70
80
90
100
110
120
y = 2x + 22
Dee
r
Acres
3. Yes;itfollowstheshapeofthedata.4.
0 5 10 15 20 25 30 35 40 45 50 55
-40
-30
-20
-10
10
20
30
40
50
60
Theplotappearsrandom,soalinearfunctionislikelyagoodfitforthedata.
AK-12North Carolina Math 1 Teacher Resource/Student Workbook Answer Key
© Walch Education
5.
0 1 2 3 4 5 6 7 8 950
100
150
200
250
300
350
400
450
500
550
600
650
700
750Ac
coun
t bal
ance
in d
olla
rs ($
)
Years
6.
0 1 2 3 4 5 6 7 8 950
100
150
200
250
300
350
400
450
500
550
600
650
700
750
Acco
unt b
alan
ce in
dol
lars
($)
Years
7. Yes;thelineappearstofollowtheshapeofthedata.
8.
0 1 2 3 4 5 6 7 8 9
-8
-6
-4
-2
2
4
6
8
Thoughitappearedthatthelinefitthedata,theU-shapeof theresidualplotindicatesthatalinearfunctionisnotagoodfitforthedata.
9.
0 2 4 6 8 10 12 14 16 18 20 22 24
20
40
60
80
100
120
140
160
180
200
220
240Ti
me
in m
inut
es
Distance in miles
AK-13North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
10.
0 2 4 6 8 10 12 14 16 18 20 22 24
-25
-20
-15
-10
-5
5
10
15
Theresidualplotisrandom,soalinearfunctionisagoodfit.
Practice 2.13 B: Analyzing Residuals1.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
60
120
180
240
300
360
420
480
540
Hei
ght i
n m
eter
s
Time in seconds
2.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
60
120
180
240
300
360
420
480
540
Hei
ght i
n m
eter
s
Time in seconds 3. Itcomesclosetothedata,butthelinedoesnotfollowthe
shapeofthedata.4.
0 1 2 3 4 5 6 7 8 9 10 11 12
-30
-20
-10
10
20
30
40
50
60
70
80
TheresidualplothasaU-shape,indicatingalinearfunctionisnotthebestfitforthedata.
AK-14North Carolina Math 1 Teacher Resource/Student Workbook Answer Key
© Walch Education
5.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 152
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34H
eigh
t in
inch
es
Age in months
6.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 152
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
Hei
ght i
n in
ches
Age in months
7. Yes;itfollowstheshapeofthedataset.
8.
0 2 4 6 8 10 12 14
-4
-3
-2
-1
1
2
3
4
Whenlookingattheresidualplot,theshapeappearstobeaU.Alinearfunctionisnotagoodfitforthedata.
9.
0 5 10 15 20 25 30 35 40 45 50 55 60 65 705
10
15
20
25
30
35
40
45
50
55
60
65
70A
rm s
pan
in in
ches
Height in inches
AK-15North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
10.
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
-4
-3
-2
-1
1
2
3
4
Theresidualplotisrandom,soalinearfunctionisagoodfit.
Lesson 2.14: Interpreting Slope and y-intercept (S–ID.7•)
Warm-Up 2.141. Slope=16;y-intercept=(0,0)2. y=16x3. –14. –2,orthepoint(0,–2)
Practice 2.14 A: Interpreting Slope and y-intercept1.
0 1 2 3 4 5 6 7 8 9100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
New
hom
es
Year
2. Answersmayvary;equationsshouldbeclosetoy=150x–120.
3. Thenumberofhomesbuilteachyearisincreasingby150.Inthiscase,whenx=0,y=–120.Thisvaluedoesnotmakesenseincontext,sincethenumberofnewhomesbuiltinayearcannotbenegative.
4. Answersmayvary;equationsshouldbeclosetoy=17.25x+7.75.
5. IttakesMadelineapproximately17minutestocompleteeachhomeworkassignment.Inthiscase,whenMadelinehasnoassignments,hertimetocompletetheassignmentswouldbe0.They-interceptdoesnotmakesenseinthiscontext.
6.
0 2 4 6 8 10 12 14 16 18 20 22 24 26 282
4
6
8
10
12
14
16
18
20
22
24
26
28
Free
thro
ws
mad
e
Free throws attempted
7. Answersmayvary;equationsshouldbeclosetoy=0.77x–0.7.
8. Willmakesapproximately77%ofhisfreethrows.Inthiscontext,ifWilldoesnotattemptanyfreethrows,hewouldnotmakeanyfreethrows;whenx=0,yshouldequal0.They-interceptisnotrelevantinthiscontext.
9. Answersmayvary;equationsshouldbeclosetoy=7.6x+3.8.
10. Ittakestheconstructioncompanyapproximately7.6weekstoconstructabuildingforeachfloorofthebuilding.Inthiscontext,ifthebuildingdoesn’thaveanyfloors,thetimetoconstructthebuildingwouldbe0;whenx=0,yshouldequal0.They-interceptisnotrelevantinthiscontext.
Practice 2.14 B: Interpreting Slope and y-intercept1.
02 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
1
2
3
4
5
6
7
8
9
Num
ber o
f win
ners
Number of players
2. Answersmayvary;equationsshouldbeclosetoy=0.19x–0.60.
AK-16North Carolina Math 1 Teacher Resource/Student Workbook Answer Key
© Walch Education
3. Aplayerwinsthegameapproximately19%ofthetime.Inthiscase,whentherearenoplayers,therewouldbenowinners;whenx=0,thenyshouldequal0.They-interceptisnotrelevantinthiscontext.
4.
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utes
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eliv
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Number of packages
5. Answersmayvary;equationsshouldbeclosetoy=0.87x+29.9.
6. Ittakesthecompanyapproximately0.87minutestodelivereachpackage.Inthiscase,iftherearenopackagestodeliver,itwouldtakenotimetodeliverthepackage;whenx=0,yshouldequal0.They-interceptisnotrelevantinthiscontext.
7. Answersmayvary;equationsshouldbeclosetoy=18.25x–6.8.
8. Eachcowproducesapproximately18litersofmilkeachday.Inthiscase,iftherearenocows,thereisnomilkproduction;whenx=0,yshouldequal0.They-interceptisnotrelevantinthiscontext.
9. Answersmayvary;equationsshouldbeclosetoy=1.80x+51.21.
10. Aperson’sheightincreasesbyapproximately1.8inchesforeachshoesize.Inthiscase,ifashoesizeis0,thereisnoheight;whenx=0,yshouldequal0.They-interceptisnotrelevantinthiscontext.
Lesson 2.15: Calculating and Interpreting the Correlation Coefficient (S–ID.8•)
Warm-Up 2.151.
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New
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nds
Number of weeks
2. Thegraphofalinearfunctionisaline.Theshapeofthedatainthegraphislinearbecausealinecouldbedrawnonthegraphwithanapproximatelyequalnumberofpointsaboveandbelowtheline.Thedataappearstohavealinearrelationship.
Practice 2.15 A: Calculating and Interpreting the Correlation Coefficient
1. strongpositivelinearcorrelation2. weakpositivelinearcorrelation3. strongnegativelinearcorrelation4. nocorrelation,orveryweaknegativelinearcorrelation5.
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Average temperature (°F)
6. Thereappearstobeapositivelinearcorrelationbetweentemperatureandplantsales.
7. r=0.848,whichindicatesthereisastrongpositivelinearcorrelationbetweentemperatureandplantsales.
AK-17North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
8.
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erag
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ol p
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att
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Number of children
9. Poolpartyattendanceappearstodecreaseasthenumberofchildrenincreases;theremaybeanegativelinearcorrelationbetweenthedata.
10. r=–0.779;thereisanegativelinearcorrelationbetweenthedata.
Practice 2.15 B: Calculating and Interpreting the Correlation Coefficient
1. weaknegativelinearcorrelation2. strongpositivelinearcorrelation3. nocorrelation4. strongnegativelinearcorrelation5.
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Poun
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Number of passengers
6. Thereappearstobeapositivelinearcorrelationbetweennumberofpassengersandpoundsofluggage.
7. r=0.92;thereisaverystrongpositivelinearcorrelationbetweenthedata.
8.
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Uni
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Magazines sold
9. Theredoesnotappeartobearelationshipbetweenthedata.10. r=–0.168;thereisnorelationshipbetweenthedata,ora
veryweaknegativelinearcorrelation.
Lesson 2.16: Distinguishing Between Correlation and Causation (S–ID.9•)
Warm-Up 2.161. Theshapeofalineargraphisastraightline.Thedata
seemstofollowastraightline,anditappearsthatthereisalinearcorrelationbetweenxandy.
2.
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Minutes spent practicing per day
3. Usingacalculator,r=–0.97.Thecorrelationcoefficientisverycloseto–1,sothereisastrongnegativelinearcorrelationbetweenxandy.
AK-18North Carolina Math 1 Teacher Resource/Student Workbook Answer Key
© Walch Education
Practice 2.16 A: Distinguishing Between Correlation and Causation
1.
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170,000
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Prod
ucts
sol
d
Advertising spending ($)
2. Thegraphappearstoberandom,withsomeincreaseinnumbersofproductssoldasadvertisingdollarsincrease.
3. r=0.311;thisindicatesthatthereisaweakpositivelinearcorrelationbetweenadvertisingdollarsspentandthenumberofproductssold.
4. Thecorrelationbetweenthetwovaluesisweak,anditisdifficulttodetermineifthereisanycausalrelationshipbetweenadvertisingdollarsspentandthenumberofproductssold.
5.
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site
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Age of client
6. Asageincreases,numberofcountriesalsoincreases;thegraphfollowsalinearshape.
7. r=0.912;thisindicatesthatthereisastrongpositivelinearcorrelationbetweenageandnumberofcountriesvisited.
8. Eventhoughthereisastrongcorrelationbetweenageandnumberofcountriesvisited,thisdoesnotmeanthatageisresponsibleforthenumberofcountriesvisited.Anolderpersonhashadmoreopportunitytotravel,buttheageoftheclientdoesnotimpactthenumberofcountriestheclienthaschosentovisit.Itisnotlikelythatthereisacausalrelationshipbetweenageandnumberofcountriesvisited.
9. Astemperatureincreases,timedecreases.Thegraphgenerallyhasalinearshapewithanegativeslope.
10. Afewfactorsinfluencethetimeittakeswatertoboil:volumeofwater,heatappliedtowater,distributionofwaterwithinitscontainer,andairpressure.Thestudentsattempttokeepthreeofthesefactorsconsistentthroughouttheexperiment,byusingidenticalcontainers,performingtheexperimentinthesameclassroom,andusingthesamevolumeofwater.Thedecreaseintimeisthereforelikelyduetotheincreaseintemperature,anditislikelythatthereisacausalrelationshipbetweentemperatureappliedandtimetoboil.
Practice 2.16 B: Distinguishing Between Correlation and Causation
1.
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200M
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f dol
lars
ear
ned
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.S. t
heat
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Millions of dollars invested
2. Thegraphappearstoberandom,withsomeincreaseindollarsearnedasdollarsinvestedincreases.
3. r=0.342;thisindicatesthatthereisaweakpositivelinearcorrelationbetweendollarsinvestedanddollarsearnedbyamovie.
4. Thecorrelationbetweenthetwovaluesisweak,anditisdifficulttodetermineifthereisanycausalrelationshipbetweendollarsinvestedanddollarsearnedinU.S.theaters.
AK-19North Carolina Math 1
Teacher Resource/Student Workbook Answer Key© Walch Education
5.
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Pairs
of s
hoes
sol
d
Salespeople
6. Thepairsofshoessoldincreasesasthenumberofsalespeopleincreases,andthegraphappearstofollowalinearshape.
7. r=0.892;thisindicatesthatthereisastrongpositivelinearcorrelationbetweennumberofsalespeopleandpairsofshoessold.
8. Sincecustomersaredependentonasalespersontohelpthemgetshoesinthecorrectsize,andthereisastrongcorrelationbetweennumberofsalespeopleandpairsofshoessold,itislikelythatthereisacausalrelationshipbetweenthetwovalues.Otherfactorsalsoinfluencethesales,buthavingmoresalespeopledirectlyimpactsthenumberofpeoplewhoareabletogetshoesinthecorrectsize,leadingtogreatershoesales.Notethateveniftherearealargenumberofsalespeople,salescannotincreaseunlesstherearecustomers.
9. Astheageofcellphoneusersincreases,thenumberofappsdecreases.Thegraphfollowsapproximatelyalinearshapewithanegativeslope.
10. Eventhoughthereappearstobeacorrelationbetweenageandnumberofapps,itisunlikelythatagecausesthereducednumberofcellphoneapps.