Question

Suppose that x=6 and y=8. If y is inversely related to x, what is y when x=3?

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} x=6\\ y=8 \end{cases}\implies 8=\cfrac{k}{6}\implies 48=k \\\\\\ therefore\qquad \boxed{y=\cfrac{48}{x}} \\\\\\ \textit{when x = 3, what is \underline{y}?}\qquad y=\cfrac{48}{3}$