Question

The pair of points is on the graph of an inverse variation. find the missing value. (5,4) and (x,7)

Answer 1

to the risk of sounding redundant.


`\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}\\\\ -------------------------------`


`\bf (5,4)\textit{ we also know that } \begin{cases} x=5\\ y=4 \end{cases}\implies 4=\cfrac{k}{5}\implies 20=k \\\\\\ therefore\qquad \boxed{y=\cfrac{20}{x}} \\\\\\ (x,7)\textit{ when y = 7, what is \underline{x}?}\qquad 7=\cfrac{20}{x}\implies x=\cfrac{20}{7}\implies x=2(6)/(7)`

Answer 2

One form of the relation of inverse variation is y = k/x.

first step: Find the value of k: Taking the values x=5 and y = 4, 4=k/5, or k=20. Then, y = 20/x.

Next: Let y = 7 and find the corresp. value of x: 7=20/x, or 7x=20, or

x = 20/7 (answer)