Question

If y varies directly as x, and y is 6 when x is 72, which is the value of y when x is 8 ?

Answer 1

$\frac{y}{x} = k$

$\frac{6}{72} = k$

$\frac{1}{12} = k$

********************************

$\frac{y}{x} = k$

$\frac{y}{8} = \frac{1}{12}$

   12y = 8

      $y = \frac{8}{12}$

      $y = \frac{2}{3}$

Answer 2

y = $\frac{2}{3}$

given y ∝ x

To convert to an equation multiply by k the constant of variation

y = kx

to find k use the given condition y = 6 when x = 72

y = kx ⇒ k = $\frac{y}{x}$ = $\frac{6}{72}$ = $\frac{1}{12}$

equation is → y = $\frac{1}{12}$ x

when x = 8 then

y = $\frac{1}{12}$ × 8 = $\frac{8}{12}$ = $\frac{2}{3}$