Question

If y varies directly with x, and y = -15 when x = -5, how do you write the direct linear variation equation and then use the equation to find x when y =12?

Answer 1

`color(green)(x=4)`

Explanation:

If `y` varies directly as `x` then
`color(white)("XXX")y=c*x` for some constant `c`

We are told that when `x=-5`, `y=-15`.
So
`color(white)("XXX")-15=c*(-5)`

`rArr`
`color(white)("XXX")c=3`

Therefore the direct variation equation is
`color(white)("XXX")y=3x`

When `y=12`
`color(white)("XXX")12=3*x`
`rArr`
`color(white)("XXX")x=4`