Question

The pair of points is on the graph of an inverse variation. Find the missing value.

(1.6, 6) and (8, y)

Answer 1

`\bf \begin{array}{llllll} \textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\ \textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\ y&=&\cfrac{{{\textit{\qquad k\qquad }}}}{}&\cfrac{}{\qquad x\qquad } &&y=\cfrac{{{ k}}}{x} \end{array} \\ \quad \\ \textit{we know that} \begin{cases} (1.6, 6)\\ -------\\ x=1.6\\ y=6 \end{cases}\implies y=\cfrac{k}{x}\implies (6)=\cfrac{k}{(1.6)}`

solve for "k", to find the "constant of variation",
and plug it back in the y = k/x, for the equation.

now, about (8,y)

namely, when x = 8, what's "y"?

well, just set x = 8, in y =k/x to get "y"

Answer 2

The missing value i.e. the value of y is:

`y=1.2`

Explanation:

We know that two variables x and y are said to be in inverse variation if there exist a constant k such that:

`y=(k)/(x)\\\\i.e.\\\\k=xy`

We are given that:

The pair of points is on the graph of an inverse variation.

The points are:

(1.6, 6) and (8, y)

i.e.

`k=6* 1.6\\\\i.e.\\\\k=9.6`

Also,

`k=8* y\\\\i.e.\\\\y=(k)/(8)\\\\i.e.\\\\y=(9.6)/(8)\\\\i.e.\\\\y=1.2`

Hence, the missing value is: 1.2