Question

Suppose y varies directly with x when x is 12 y is 14 write the equation that relates x and y

Answer 1

Given that 'y' is directly proportional to 'x',

`y\propto x`

Let 'k' be the constant of proportionality.

Then the equation becomes,

`y=kx`

Given that 'y' is 14 when 'x' is 12,

`\begin{gathered} x=12 \\ y=14 \end{gathered}`

Substitute the values in the equation,

`\begin{gathered} 14=k\cdot12 \\ k=(14)/(12) \\ k=(7)/(6) \end{gathered}`

Substitute the value of 'k' in the equation,

`y=(7)/(6)x`

Thus, the required equation that relates 'x' and 'y' is,

`y=(7)/(6)x`