Question

The pair of points is on the graph of an inverse variation. Find the missing value. (1.6, 6) and (8, y) 0.03 30 1.2 0.83

Answer 1

Answer: 1.2

Step-by-step explanation:

The formula for inverse variation  is given by :-

$x_1y_1=x_2y_2$

The given points : (1.6, 6) and (8, y)

It means at x = 1.6 , y=6 .

To find the value of y at x=8 , we substitute $x_1=1.6,\ y_1=6\, \text{ and}\ x_2=8,\ y_2=y$ in the above formula , we get

$1.6\times6=8y\\\\\Rightarrow\ y=\dfrac{1.6\times6}{8}\\\\\Rightarrow\ y=1.2$

Thus, the missing value = 1.2

Answer 2

One may note that (1.6 , 6)  is just another way to say x = 1.6 when y = 6.

and that (8 , y) is another way to say x = 8 and y is who knows.

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \textit{we know that } \begin{cases} x=1.6\\ y=6 \end{cases}\implies 6=\cfrac{k}{1.6}\implies 6(1.6)=k\implies 9.6=k \\\\\\ \qquad therefore\qquad \boxed{y=\cfrac{9.6}{x}} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad y=\cfrac{9.6}{8}$