Question

If x and y vary inversely, and x = -12 when y = ³/2, what is y when x = 2?

Answer 1

`x\propto(1)/(y)`

Therefore,

`xy=k\text{ where k is a constant}`

Then,

`x_1y_1=x_2y_2`

In this case,

`x_1=-12,y_1=(3)/(2),x_2=2,y_2=\text{?}`
`2y_2=-12((3)/(2))=-6*3=-18`

this implies that

`\begin{gathered} (2y_2)/(2)=(-18)/(2) \\ \text{therefore} \\ y_2=-9 \end{gathered}`

Therefore, when x = 2, y = -9