How do you determine whether y varies directly with x and if so, how do you find the constant of variation k for $- 5 y = 5 x + 10$ $- 5y = 5x + 10$ ?

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How do you determine whether y varies directly with x and if so, how do you find the constant of variation k for $- 5 y = 5 x + 10$ $- 5y = 5x + 10$ ?

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Answer 1 · 2015-04-09T19:39:27

$- 5 y = 5 x + 10$ $-5y = 5x +10$
could be simplified as
$y = - x - 2$ $y = -x -2$

According to
http://www.merriam-webster.com/dictionary/direct%20variation
Definition of DIRECT VARIATION
: mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other

from which it follows that the given equation is not a direct variation (i.e. $y$ $y$ does not vary directly with $x$ $x$ ).

The equation of a line parallel to this which would be a direct variation would be
$y = - x$ $y =-x$
or $y = (- 1) x$ $y= (-1)x$
and for this equation the constant of variation would be $(- 1)$ $(-1)$

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How do you determine whether y varies directly with x and if so, how do you find the constant of variation k for $- 5 y = 5 x + 10$ $- 5y = 5x + 10$ ?

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How do you determine whether y varies directly with x and if so, how do you find the constant of variation k for −5y=5x+10- 5y = 5x + 10?

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How do you determine whether y varies directly with x and if so, how do you find the constant of variation k for $- 5 y = 5 x + 10$ $- 5y = 5x + 10$ ?