50 POINTS
This table represents a proportional relationship.

What is the constant of proportionality for this proportional relationship?
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50 POINTS This table represents a proportional relationship What is the constant of proportionality for this proportional relationship 110 89 10 class=

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[tex]\huge \sf༆ Answer ༄[/tex]

According to the question ;

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y \propto x[/tex]

Now, let's add a constant of proportionality to replace proportionality sign with equal to :

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = kx[/tex]

[ where, k is proportionality constant ]

plug the value of x and y from any ordered pair in the table , for example : [tex] \sf(\dfrac{1}{5} , 2)[/tex]

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:2 = k \times \dfrac{1}{5} [/tex]

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:k = 2 \times 5[/tex]

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:k = 10[/tex]

Therefore, value of proportionality constant (k) is

[tex]\overbrace{  \underbrace{\underline{ \boxed{ \sf 10 }}}}[/tex]