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TEK 7.4CConstant of Proportionality
ThisproducthitsthefollowingTEK:7.4CDeterminetheconstantofproportionality(k=y/x)withinmathematicalandreal-worldproblems.
Thisproductincludes3versionsofthefoldable:• Pg.2-3– completednotes• Pg.3-4– noteswithoutexamples• Pg.5-6– onlythequestions• Pg.7-8– Answerkeytothefoldable
PrintingInstructions:• Selectpagesyouwanttoprint• Printdouble-sided
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q Unit rate
q Constantrateofchange– aratiowhenthedependent,y-value,changesataconstantrateforeachindependent,x- value
ConstantofProportionalityAconstantofproportionalityisaconstantratiobetw
een2proportionalquantitiesdenoted
bythesymbolk
y =kx
Yis they-value(x,y)KistheConstantorProportionalityXisthex-value(x,y)
AProportionalRelationshipshasaconstantrateofchangewith thefollowingcharacteristics:• Linear– straight line• Passesthroughtheorigin(0,0)• Representedbyy=kx
ProportionalorNotfromaTable?1) Writetherates2) Comparetherates3) Iftheratesareallequal,thenthe
relationshipisproportional.
Constantofproportionality=k=𝒚𝒙
ProportionalorNotfromWords?1) Writetherates2) Comparetherates3) Iftheratesareallequal,thenthe
relationshipisproportional.
Constantofproportionality=k=𝒚𝒙
Twopounds ofalmondscost$14,and8poundscost$56.
Ifthereisaproportionalrelationshipbetweenxandy,youcandescribethatrelationshipusing the equation:y=kx.
Sowriteanequation fortheverbaldescriptionabove↑
Proportional orNotfromaGraph?1. Doesitgothroughtheorigin?2. Isitastraightline?
Thenyes,itisproportional!
Milestraveled
hours
0
1
2
3
0 1 2 3 4 5
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SynonymsforConstantofProportionality
What isaLinearProportionalRelationship?
Howtodeterminetheconstant ofproportionalityfromaTabular
representation?(table)
How todeterminetheconstantofproportionalityfromaVerbalrepresentation?(words)
HowtowriteanAlgebraicrepresentationforaProportional
Relationship?(Equation)
Graphical (graph)
![Page 4: 7.4C Constant of Proportionality Foldable · q Constant rate of change –a ratio when the dependent, y-value, changes at a constant rate for each independent, x-value ty s a ed k](https://reader033.vdocuments.us/reader033/viewer/2022042913/5f4b13f62734317e1b381544/html5/thumbnails/4.jpg)
q Unit rate
q Constantrateofchange– aratiowhenthedependent,y-value,changesataconstantrateforeachindependent,x- value
ConstantofProportionalityAconstantofproportionalityisaconstantratiobetw
een2proportionalquantitiesdenoted
bythesymbolk
y =kx
Yis they-value(x,y)KistheConstantorProportionalityXisthex-value(x,y)
AProportionalRelationshipshasaconstantrateofchangewith thefollowingcharacteristics:• Linear– straight line• Passesthroughtheorigin(0,0)• Representedbyy=kx
ProportionalorNotfromaTable?1) Writetherates2) Comparetherates3) Iftheratesareallequal,thenthe
relationshipisproportional.
Constantofproportionality=k=𝒚𝒙
ProportionalorNotfromWords?1) Writetherates2) Comparetherates3) Iftheratesareallequal,thenthe
relationshipisproportional.
Constantofproportionality=k=𝒚𝒙
Ifthereisaproportionalrelationshipbetweenxandy,youcandescribethatrelationshipusing the equation:y=kx.
Proportional orNotfromaGraph?1. Doesitgothroughtheorigin?2. Isitastraightline?
Thenyes,itisproportional!
![Page 5: 7.4C Constant of Proportionality Foldable · q Constant rate of change –a ratio when the dependent, y-value, changes at a constant rate for each independent, x-value ty s a ed k](https://reader033.vdocuments.us/reader033/viewer/2022042913/5f4b13f62734317e1b381544/html5/thumbnails/5.jpg)
SynonymsforConstantofProportionality
What isaLinearProportionalRelationship?
Howtodeterminetheconstant ofproportionalityfromaTabular
representation?(table)
How todeterminetheconstantofproportionalityfromaVerbalrepresentation?(words)
HowtowriteanAlgebraicrepresentationforaProportional
Relationship?(Equation)
Graphical (graph)
![Page 6: 7.4C Constant of Proportionality Foldable · q Constant rate of change –a ratio when the dependent, y-value, changes at a constant rate for each independent, x-value ty s a ed k](https://reader033.vdocuments.us/reader033/viewer/2022042913/5f4b13f62734317e1b381544/html5/thumbnails/6.jpg)
ConstantofProportionalityAconstantofproportionalityisaconstantratiobetw
een2proportionalquantitiesdenoted
bythesymbolk
![Page 7: 7.4C Constant of Proportionality Foldable · q Constant rate of change –a ratio when the dependent, y-value, changes at a constant rate for each independent, x-value ty s a ed k](https://reader033.vdocuments.us/reader033/viewer/2022042913/5f4b13f62734317e1b381544/html5/thumbnails/7.jpg)
SynonymsforConstantofProportionality
What isaLinearProportionalRelationship?
Howtodeterminetheconstant ofproportionalityfromaTabular
representation?(table)
How todeterminetheconstantofproportionalityfromaVerbalrepresentation?(words)
HowtowriteanAlgebraicrepresentationforaProportional
Relationship?(Equation)
Graphical (graph)
![Page 8: 7.4C Constant of Proportionality Foldable · q Constant rate of change –a ratio when the dependent, y-value, changes at a constant rate for each independent, x-value ty s a ed k](https://reader033.vdocuments.us/reader033/viewer/2022042913/5f4b13f62734317e1b381544/html5/thumbnails/8.jpg)
q Unit rate
q Constantrateofchange– aratiowhenthedependent,y-value,changesataconstantrateforeachindependent,x- value
ConstantofProportionalityAconstantofproportionalityisaconstantratiobetw
een2proportionalquantitiesdenoted
bythesymbolk
y =kx
Yis they-value(x,y)KistheConstantorProportionalityXisthex-value(x,y)
AProportionalRelationshipshasaconstantrateofchangewith thefollowingcharacteristics:• Linear– straight line• Passesthroughtheorigin(0,0)• Representedbyy=kx
ProportionalorNotfromaTable?1) Writetherates2) Comparetherates3) Iftheratesareallequal,thenthe
relationshipisproportional.
Constantofproportionality=k=𝒚𝒙
𝑘 = 𝑦𝑥 =
𝑚𝑖𝑙𝑒𝑠ℎ𝑜𝑢𝑟 =
501 =
751.5 = 50
ProportionalorNotfromWords?1) Writetherates2) Comparetherates3) Iftheratesareallequal,thenthe
relationshipisproportional.
Constantofproportionality=k=𝒚𝒙
Twopounds ofalmondscost$14,and8poundscost$56.
𝐾 = 𝑦𝑥 =
𝑐𝑜𝑠𝑡𝑝𝑜𝑢𝑛𝑑 =
$142 =
$568 = $7
$7perpoundofalmonds
Ifthereisaproportionalrelationshipbetweenxandy,youcandescribethatrelationshipusing the equation:y=kx.
Sowriteanequation fortheverbaldescriptionabove↑
y =kx↓
y=$7x
Proportional orNotfromaGraph?1. Doesitgothroughtheorigin?2. Isitastraightline?
Thenyes,itisproportional!
Milestraveled 50 75
hours 1 1.5
0
1
2
3
0 1 2 3 4 5
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SynonymsforConstantofProportionality
What isaLinearProportionalRelationship?
Howtodeterminetheconstant ofproportionalityfromaTabular
representation?(table)
How todeterminetheconstantofproportionalityfromaVerbalrepresentation?(words)
HowtowriteanAlgebraicrepresentationforaProportional
Relationship?(Equation)
Graphical (graph)