The variable y varies inversely as x. If y = 6 when x = 4, what is the value of y when x =… — JAMB UTME

The variable $y$ varies inversely as $x$ . If $y = 6$ when $x = 4$ , what is the value of $y$ when $x = 8$ ?

The value of

y

when

x = 8

is 3.

Since

y

varies inversely as

x

, the formula connecting them is

y = \frac{k}{x}

. Substituting

y = 6

when

x = 4

gives

6 = \frac{k}{4}

, which yields

k = 24

. Using this constant, when

x = 8

y = \frac{24}{8} = 3

Write the relationship for inverse variation.

y = \frac{k}{x}

Inverse variation means

y

is inversely proportional to

x

, where

k

is the constant of variation.

Substitute given values

y = 6

and

x = 4

to solve for

k

6 = \frac{k}{4} \implies k = 6 \times 4 = 24

To complete the equation of variation, the constant

k

must be determined.

Substitute

k = 24

and

x = 8

into the variation equation to find

y

y = \frac{24}{8} = 3

Evaluating the relationship at

x = 8

gives the requested value.

Inverse Variation

Question