Question

If y varies inversely as x. When y = 12, x = 7. How do you find the constant of variation and use it to determine the value for y when x = 4?

Answer 1

The constant of variation is `84`
When `x=4` then `y=21`

Explanation:

If `y` varies inversely as `x` then
`color(white)("XXX")xy=c` for some constant of variation `c`

We are told `(x,y)=(7,12)` is a solution for this equation so
`color(white)("XXX")7xx12=c`
`rArr` `color(white)("XXX")c=84`

When `x=4`
`color(white)("XXX")4y=84`
`rArr` `color(white)("XXX")y=21`