Question

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

y = –3x or ,
y = –x/3 or,
y = x/3 or,
y = 3x .

Answer 1

I would say the third one. Plug in the x values:

y = -9/3

-9/3 = -3

y = -3

(-9, -3)

The equation is true.

Answer 2

Answer: (c)
`y=(x)/(3).`

Step-by-step explanation: Given that,

`(-9,-3)~\textup{and}~(-12,-4)` are two points contained in the function. Since it is a direct variation function, so it is a straight line passing through the given points.

Let,
`x_(1)=-9,~y_(1) =-3,~x_(2)=-12~\textup{and}~y_(2) =-4.`

So, slope of the line is given by

`m=(y_(2)-y_(1) )/(x_(2) -x_(1) ) \\\Rightarrowc=(1)/(3).`

The equation of the line or the function is

`y-y_(1) =m(x-x_(1) )\\\Rightarrow y+3 =(1)/(3)(x+9 )\\\Rightarrow3y+9=x+9\\\Rightarrow3y=x\\\Rightarrow y=(x)/(3).`

Thus, (c)
`y=(x)/(3)` is the correct option.