Question

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

Answer 1

Answer: (c) $y=\dfrac{x}{3}.$

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

$m=\dfrac{y_{2}-y_{1} }{x_{2} -x_{1} } \\\Rightarrowc=\dfrac{1}{3}.$

The equation of the line or the function is

$y-y_{1} =m(x-x_{1} )\\\Rightarrow y+3 =\frac{1}{3}(x+9 )\\\Rightarrow3y+9=x+9\\\Rightarrow3y=x\\\Rightarrow y=\frac{x}{3}.$

Thus, (c)  $y=\dfrac{x}{3}$ is the correct option.

Answer 2

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.