Question

Y varies directly with x. y=24 when x=6. Find y when x=8.

Answer 1

Y varies directly with x.

This can be represented below as

`\begin{gathered} y\propto x \\ y=kx \end{gathered}`

Substitute the value of y=24 and x=6 to find the value of k

`\begin{gathered} y=kx \\ 24=6k \\ divide\text{ both sides by 6} \\ (6k)/(6)=(24)/(6) \\ k=4 \end{gathered}`

Substitute k=4 to get the equation connecting y and x

`\begin{gathered} y=kx \\ y=4x \end{gathered}`

Substitute the value of x=8 to get the value of y

`\begin{gathered} y=4x \\ y=4*8 \\ y=32 \end{gathered}`

Hence,

The value of y when x= 8 is

`\Rightarrow y=32`