Question

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

y=-*
y=-x
y = x
O y = fx

Answer 1

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

Explanation:

The direct variation is defined as

`y\propto x`

`y=kx`

where, k is constant of proportionality.

It is given that a direct variation function contains the points (-8,-6) and (12, 9).

Substitute x=-8 and y=-6 in the above equation.

`-6=-8k`

Divide both sides by -8.

`(-6)/(-8)=k`

`(3)/(4)=k`

The value of constant of proportionality is
`(3)/(4)`. So, the required equation is

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

At x=12,

`y=(3)/(4)(12)=9`

It means, the line passing through (12,9). Hence, the equation is correct.

Therefore, the equation of the function is
`y=(3)/(4)x`.