Question

Write an appropriate inverse variation equation if y = 7 when x = 2.

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\\ variation \end{array}\\\\ -------------------------------\\\\ \textit{we know that } \begin{cases} y=7\\ x=2 \end{cases}\implies 7=\cfrac{k}{2}\implies 7\cdot 2=k\implies 14=k \\\\\\ thus\qquad \qquad \boxed{y=\cfrac{14}{x}}`