TEK 7.4CConstant of Proportionality

ThisproducthitsthefollowingTEK:7.4CDeterminetheconstantofproportionality(k=y/x)withinmathematicalandreal-worldproblems.

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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

SynonymsforConstantofProportionality

What isaLinearProportionalRelationship?

Howtodeterminetheconstant ofproportionalityfromaTabular

representation?(table)

How todeterminetheconstantofproportionalityfromaVerbalrepresentation?(words)

HowtowriteanAlgebraicrepresentationforaProportional

Relationship?(Equation)

Graphical (graph)

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!

SynonymsforConstantofProportionality

What isaLinearProportionalRelationship?

Howtodeterminetheconstant ofproportionalityfromaTabular

representation?(table)

How todeterminetheconstantofproportionalityfromaVerbalrepresentation?(words)

HowtowriteanAlgebraicrepresentationforaProportional

Relationship?(Equation)

Graphical (graph)

ConstantofProportionalityAconstantofproportionalityisaconstantratiobetw

een2proportionalquantitiesdenoted

bythesymbolk

SynonymsforConstantofProportionality

What isaLinearProportionalRelationship?

Howtodeterminetheconstant ofproportionalityfromaTabular

representation?(table)

How todeterminetheconstantofproportionalityfromaVerbalrepresentation?(words)

HowtowriteanAlgebraicrepresentationforaProportional

Relationship?(Equation)

Graphical (graph)

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

SynonymsforConstantofProportionality

What isaLinearProportionalRelationship?

Howtodeterminetheconstant ofproportionalityfromaTabular

representation?(table)

How todeterminetheconstantofproportionalityfromaVerbalrepresentation?(words)

HowtowriteanAlgebraicrepresentationforaProportional

Relationship?(Equation)

Graphical (graph)