Is $x - 3 y = 0$ $x-3y=0$ a direct variation equation and if so, what is the constant of variation?

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Is $x - 3 y = 0$ $x-3y=0$ a direct variation equation and if so, what is the constant of variation?

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Answer 1 · 2018-05-02T06:27:06

Yes, it is a direct variation. See explanation.

Explanation:

A direct variation is any function in a form:

$f (x) = a x$ $f(x)=ax$

The given function is:

$x - 3 y = 0$ $x-3y=0$

To transform it to $y = a x$ $y=ax$ we do:

$x - 3 y = 0$ $x-3y=0$

$x = 3 y$ $x=3y$

$y = \frac{1}{3} x$ $y=1/3x$

This proves that the function is a direct variation and the constant of variation is:

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Is $x - 3 y = 0$ $x-3y=0$ a direct variation equation and if so, what is the constant of variation?

1 Answer

Explanation:

$f (x) = a x$ $f(x)=ax$

$x - 3 y = 0$ $x-3y=0$

$x - 3 y = 0$ $x-3y=0$

$x = 3 y$ $x=3y$

$y = \frac{1}{3} x$ $y=1/3x$

$a = \frac{1}{3}$ $a=1/3$

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Is x-3y=0x−3y=0x-3y=0 a direct variation equation and if so, what is the constant of variation?

1 Answer

Explanation:

f(x)=axf(x)=axf(x)=ax

x-3y=0x−3y=0x-3y=0

x-3y=0x−3y=0x-3y=0

x=3yx=3yx=3y

y=1/3xy=13xy=1/3x

a=1/3a=13a=1/3

Related questions

Impact of this question

Is $x - 3 y = 0$ $x-3y=0$ a direct variation equation and if so, what is the constant of variation?

$f (x) = a x$ $f(x)=ax$

$x - 3 y = 0$ $x-3y=0$

$x - 3 y = 0$ $x-3y=0$

$x = 3 y$ $x=3y$

$y = \frac{1}{3} x$ $y=1/3x$

$a = \frac{1}{3}$ $a=1/3$