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,

$\begin{gathered} 14=k\cdot12 \\ k=\frac{14}{12} \\ k=\frac{7}{6} \end{gathered}$

Substitute the value of 'k' in the equation,

$y=\frac{7}{6}x$

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

$y=\frac{7}{6}x$