beautifulmess44
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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 .

Respuesta :

Mehek
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: (c) [tex]y=\dfrac{x}{3}.[/tex]


Step-by-step explanation: Given that,

[tex](-9,-3)~\textup{and}~(-12,-4)[/tex] 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, [tex]x_{1}=-9,~y_{1} =-3,~x_{2}=-12~\textup{and}~y_{2} =-4.[/tex]

So, slope of the line is given by

[tex]m=\dfrac{y_{2}-y_{1} }{x_{2} -x_{1} } \\\Rightarrowc=\dfrac{1}{3}.[/tex]

The equation of the line or the function is

[tex]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}.[/tex]

Thus, (c)  [tex]y=\dfrac{x}{3}[/tex] is the correct option.