Question

A direct variation function contains the points (-9, -3) and (-12,-4). Which equation represents the function?

y= -3х

Answer 1

`y=(1)/(3)x`

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have the ordered pairs

(-9,-3) and (-12,-4)

Find the value of the constant of proportionality k

`k=(y)/(x)`

For x=-9, y=-3 ---->
`k=(-3)/(-9)=(1)/(3)`

For x=-12, y=-4 ---->
`k=(-4)/(-12)=(1)/(3)`

so

The value of k is equal to
`(1)/(3)`

The linear equation is

`y=(1)/(3)x`