Question

What is the constant of proportionality in the equation StartFraction x over y EndFraction StartFraction 2 over 9 EndFraction?

Answer 1

Given:

The equation is:

$\dfrac{x}{y}=\dfrac{2}{9}$

To find:

The constant of proportionality.

Solution:

If y is directly proportional to x, then

$y\propto x$

$y=kx$                        ...(i)

Where, k is the constant of proportionality.

We have,

$\dfrac{x}{y}=\dfrac{2}{9}$

On cross multiplication, we get

$9x=2y$

Divide both sides by 2.

$\dfrac{9}{2}x=y$

Interchange the sides.

$y=\dfrac{9}{2}x$                ...(ii)

On comparing (i) and (ii), we get

$k=\dfrac{9}{2}$

The constant of proportionality is $\dfrac{9}{2}$. Therefore, the correct option is B.