Question

Question #2f3ee

Answer 1

This table does represent direct variation with a constant `k=-3`.

Explanation:

Direct variation is of the form `y=kx`, where `k` is the constant of variation.

All of the values in the table satisfy `y=-3x`, so this does express a direct variation. In this case the constant of variation is `k=-3`.

Answer 2

`k=-3" and "y=-3x`

Explanation:

`"for direct variation "ypropx`

`"to convert to an equation multiply by k the constant"`
`"of variation"`

`rArry=kx`

`"to find k check the given values in the table"`

`rArrk=y/x`

`y=-3,x=-1rArrk=-3`

`y=-6,x=2rArrk=(-6)/2=-3`

`y=-9,x=3rArrk=(-9)/3=-3`

`y=-12,x=4rArrk=(-12)/4=-3`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=-3x)color(white)(2/2)|)))`