Question

The equation y = 1/2x represents a proportional relationship. What is the constant of proportionality?​

Answer 1

$\underline{ \pink{ Direct \: variation : }}$

$If \: x \: and \: y \: are \: any \:two \: quantities \\such \:that \: both\:of \:them \: increase \:or \\decrease \: together \:and \: \frac{x}{y} \:remains \\constant \: (say \:k) , \:then \: x \: and \: y \:are \:in \\direct \: proportion.$

$This \: can \: be \: written \: as \: x \:propto y \\and \: read \: as \:x \: is \: directly \: proportional \\to \: y$

$\blue{ \frac{x}{y} = k \implies x = ky},$

$where \: k \: is \: constant \: of \: proportion.$

$Here, Given \: equation \: y = \frac{1}{2} x$

$\red{ Constant \:of \: Proportionality } \green { = \frac{1}{2}}$

$Option \: \pink{ ( c ) } \: is \: correct.$

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Answer 2

Answer:

Directvariation:

\begin{gathered}If \: x \: and \: y \: are \: any \:two \: quantities \\such \:that \: both\:of \:them \: increase \:or \\decrease \: together \:and \: \frac{x}{y} \:remains \\constant \: (say \:k) , \:then \: x \: and \: y \:are \:in \\direct \: proportion.\end{gathered}

Ifxandyareanytwoquantities

suchthatbothofthemincreaseor

decreasetogetherand

y

x

remains

constant(sayk),thenxandyarein

directproportion.

\begin{gathered}This \: can \: be \: written \: as \: x \:propto y \\and \: read \: as \:x \: is \: directly \: proportional \\to \: y\end{gathered}

Thiscanbewrittenasxproptoy

andreadasxisdirectlyproportional

toy

\blue{ \frac{x}{y} = k \implies x = ky},

y

x

=k⟹x=ky,

where \: k \: is \: constant \: of \: proportion.wherekisconstantofproportion.

Here, Given \: equation \: y = \frac{1}{2} xHere,Givenequationy=

2

1

x

\red{ Constant \:of \: Proportionality } \green { = \frac{1}{2}}ConstantofProportionality=

2

1

Option \: \pink{ ( c ) } \: is \: correct.Option(c)iscorrect.

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