Question

Suppose that a y varies inversely with x, and y=6 when x=8. What is an equation for the inverse variation?

Answer 1

`y=1/x+47/8`

Explanation:

`y` varies inversely as `x`, therefore
`y=1/x+c`, where `c` is an unknown constant

substitute `y` for 6 and `x` for 8:
`6=1/8+c`
`6-1/8=1/8+c-1/8`
`((6xx8)-1)/8=c`
`(48-1)/8=c`
`47/8=c`

replace `c` with `47/8` in `y=1/x+c`
answer: `y=1/x+47/8`