Question

Assume that y varies inversely as x. If y = -6 when x = -2, how do you find y when x = 5?

Answer 1

At `x=5 "; "y=12/5 = 2 2/5`

Explanation:

This is a version ratios (ratios turn up all over the place).

Consider the example: `a/b=c/d => a=bxxc/d`

This is exactly what we have in this question.

Let `k` be a constant

`y=kxx1/x`

`color(green)(y=k/x)` ...................................(1)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the value of "k)`

Given condition: at `y=-6" "x=-2`

Substituting in equation (1)

`" "-6=k/(-2)`

Multiply both sides by 2

`(-6)xx2=kxx 2/(-2)`

But `2/(-2)=-1`

`=>-12=-k`

So `k=+12`

Thus equation (1) becomes

`color(green)(y=12/x)`.................................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So at `x=5` we have:

`" "y=12/5 = 2 2/5`