Question

x varies directly as y, when x = 5, y = 30. Find the constant of variation and equation of variation.

Answer 1

Hi,

solution:

According to question , x is directly proportional to y.
Equation of variation:
➖➖➖➖➖➖➖➖
$x \: \: \alpha \: \: y$
when we remove proportional symbol
$x \: \: \: = \: \: c \: y$
here, c is proportionality constant.

so value of constant c is given by:
Value of proportionality constant:
➖➖➖➖➖➖➖➖➖➖➖➖
$c = \frac{x}{y}$
value given as x = 5

y = 30

$c = \frac{5}{30} \\ \\ c = \frac{1}{6}$
hope it helps you.

Answer 2

Solution ;

It is given that , x ∝ y

x /y = k [ k is a constant of variation ] ----- ( 1 )

Now ,

Substitute x = 5 , y = 30 in ( 1 ) , we get

k = 5/30 = 1/6

∴ Constant Variation ( k ) = 1/6

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