Question

. x ∝ y. When x = 4, y = 20. Find the constant of variation and the equation of variation.​

Answer 1

SOLUTION

GIVEN

x ∝ y When x = 4, y = 20.

TO DETERMINE

• The constant of variation

• The equation of variation.

EVALUATION

Here it is given that

x ∝ y

⇒ x = ky - - - - - - (1)

where k is constant of variation

Now it is given that when x = 4 , y = 20.

We get from Equation 1

4 = k × 20

$\displaystyle \sf{ \implies k = \frac{4}{20} }$

$\displaystyle \sf{ \implies k = \frac{1}{5} }$

$\displaystyle \sf{The \: constant \: of \: variation \: = \frac{1}{5} }$

From Equation 1 we get

$\sf x = \dfrac{y}{5}$

Which is the required equation of variation.

FINAL ANSWER

$\displaystyle \sf{The \: constant \: of \: variation \: = \frac{1}{5} }$

The equation of variation

$\sf x = \dfrac{y}{5}$

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