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Sagot :
Given:
The equation is:
[tex]\dfrac{x}{y}=\dfrac{2}{9}[/tex]
To find:
The constant of proportionality.
Solution:
If y is directly proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is the constant of proportionality.
We have,
[tex]\dfrac{x}{y}=\dfrac{2}{9}[/tex]
On cross multiplication, we get
[tex]9x=2y[/tex]
Divide both sides by 2.
[tex]\dfrac{9}{2}x=y[/tex]
Interchange the sides.
[tex]y=\dfrac{9}{2}x[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]k=\dfrac{9}{2}[/tex]
The constant of proportionality is [tex]\dfrac{9}{2}[/tex]. Therefore, the correct option is B.
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