Is 3y=9x a direct variation and if so, what is the constant?

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Is 3y=9x a direct variation and if so, what is the constant?

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Answer 1 · 2018-04-13T07:55:19

$k = 3$ $k=3$

Explanation:

$a direct variation equation has the form$ $"a direct variation equation has the form"$

$∙ x y = k x \leftarrow k is the constant of variation$ $•color(white)(x)y=kxlarrcolor(blue)"k is the constant of variation"$

$3 y = 9 x \leftarrow divide both sides by 3$ $3y=9xlarrcolor(blue)"divide both sides by 3"$

$\Rightarrow y = 3 x$ $rArry=3x$

$this is a direct variation equation with k = 3$ $"this is a direct variation equation with "k=3$

Answer 2 · 2018-04-13T08:01:45

Yes, it is. And constant is 3. See below

Explanation:

$3 y = 9 x$ $3y=9x$ is a direct variation because for two diferente values values of $x$ $x$ , lets say $x_{0}$ $x_0$ and $x_{1}$ $x_1$ we have

$3 y_{0} = 9 x_{0}$ $3y_0=9x_0$ and $3 y_{1} = 9 x_{1}$ $3y_1=9x_1$ substracting both we have

$3 y_{0} - 3 y_{1} = 9 x_{0} - 9 x_{1}$ $3y_0-3y_1=9x_0-9x_1$

$3 (y_{0} - y_{1}) = 9 (x_{0} - x_{1})$ $3(y_0-y_1)=9(x_0-x_1)$ from here we have

$\frac{y_{0} - y_{1}}{x_{0} - x_{1}} = \frac{9}{3} = 3$ $(y_0-y_1)/(x_0-x_1)=9/3=3$

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Is 3y=9x a direct variation and if so, what is the constant?

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