Question

y varies inversely with x. If x is 2.3 when y is 5.1, what is k, the constant of inverse variation? Round your answer to the nearest hundredth, if necessary.

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} x=2.3\\ y=5.1 \end{cases}\implies 5.1=\cfrac{k}{2.3}\implies (5.1)(2.3)=k$

Answer 2

y varies inversely with x → $y= \frac{k}{x}$ where k is the constant of variation 

5.1 = k/2.3 ← substitute values into the formula

k = 11.73 ← result of multiplying both sides by 2.3

ANSWER: k = 11.73