How do you tell if an equation like $x + 7 y = 0$ $x+7y=0$ or $2 x + 3 y = 1$ $2x+3y=1$ is a direct variation?

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How do you tell if an equation like $x + 7 y = 0$ $x+7y=0$ or $2 x + 3 y = 1$ $2x+3y=1$ is a direct variation?

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Answer 1 · 2015-04-11T20:53:58

If an equation can be manipulated into the form
$y = m \cdot x$ $y = m*x$ for some constant $m$ $m$ then it is a direct variation (otherwise it is not).

To use your examples:
$x + 7 y = 0$ $x+7y=0$
$\to 7 y = - x$ $rarr 7y= -x$
$\to y = (- \frac{1}{7}) x$ $rarr y = (-1/7)x$
So this is a direct variation (with $m = (- \frac{1}{7})$ $m=(-1/7)$ )

$2 x + 3 y = 1$ $2x+3y = 1$
$\to 3 y = - 2 x + 1$ $rarr 3y = -2x +1$
$\to y = (- \frac{2}{3}) x + \frac{1}{3}$ $rarr y = (-2/3)x +1/3$
Because of the additional term $+ \frac{1}{3}$ $+1/3$ this can not be expressed as $y$ $y$ equal to a constant multiplied by x.
So this is not a direct variation.

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How do you tell if an equation like $x + 7 y = 0$ $x+7y=0$ or $2 x + 3 y = 1$ $2x+3y=1$ is a direct variation?

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