Does the equation $3 x + 5 y = 0$ $3x+5y=0$ represent a direct variation and if so, identify the constant of variation?

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Answer 1 · 2016-05-13T18:52:54

The constant of variation is $\frac{3}{5}$ $3/5$
I will let you decide if this is positive or negative. See explanation as to why.

Given: $3 x + 5 y = 0$ $3x+5y=0$

Subtract $3 x$ $3x$ from both sides

$3 x - 3 x + 5 y = 0 - 3 x$ $3x-3x+5y=0-3x$

#0+5y=-3x

$5 y = - 3 x$ $5y=-3x$

Divide both sides by 5

$\frac{5}{5} \times y = - \frac{3}{5} x$ $5/5xxy=-3/5x$

But $\frac{5}{5} = 1$ $5/5=1$

$y = - \frac{3}{5} x$ $y=-3/5x$

If you wish the $x$ $x$ to be positive: multiply both sides by $(- 1)$ $(-1)$

$- y = + \frac{3}{5} x$ $-y=+3/5x$

The constant of variation is $\frac{3}{5}$ $3/5$

Does the equation 3x+5y=03x+5y=0 represent a direct variation and if so, identify the constant of variation?