Question

A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function?

y = –4/3x
y = –3/4x
y = 3/4x
y =4/3 x

Answer 1

`y=(3)/(4)x`

Explanation:

If it is a direct variation function, then
`(y)/(x)=k`.

`k` can be found by choosing a point and doing
`y` divided by
`x`.

So we can find
`k` by doing -6 divided by -8 or 9 divided by 12.

Both of these values are equal to 0.75 or 3/4 as a fraction.

So you can say any point in this relation will follow the equation:

`(y)/(x)=(3)/(4)`

Multiply both sides by
`x`:

`y=(3)/(4)x`