Question

If y varies directly with x, write an equation for the direct variation. Then find the value.

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that}~~ \begin{cases} y=3\\ x=2 \end{cases}\implies 3=k2\implies \cfrac{3}{2}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{3}{2}x} \\\\\\ \textit{when x = 1, what is \underline{y}?}\qquad y=\cfrac{3}{2}(1)\implies y=\cfrac{3}{2}$

Answer 2

since y varies directly with y then

y = kx ( k is the constant of variation )

to find k use y = 3 when x = 2

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

equation is : y = $\frac{3}{2}$ x

When x = 1 then y = $\frac{3}{2}$ × 1 = $\frac{3}{2}$