Question

If y varies inversely as x, and y=10 when x=2, find y when x=8

Answer 1

If it varies inversely, then their product is the same. So,
10*2 = y*8
20 = y*8
 /8      /8
5/2 = y
y = 2.5

Answer 2

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=10\\ x=2 \end{cases}\implies 10=k2\implies \cfrac{10}{2}=k\implies 5=k \\\\\\ therefore\qquad \boxed{y=\cfrac{5}{x}} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad y=\cfrac{5}{8}$