# Is #5x = -3y# a direct variation equation and if so, what is the constant of variation?

The graph of your function:

graph{(-5x)/3 [-5, 5, -5, 5]}

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Yes, the equation (5x = -3y) represents a direct variation. The constant of variation can be found by rearranging the equation into the form (y = kx), where (k) represents the constant of variation.

To do this, divide both sides of the equation by -3:

[ \frac{5x}{-3} = \frac{-3y}{-3} \implies \frac{-5}{3}x = y ]

Comparing this with the standard form of a direct variation equation (y = kx), we see that (k = \frac{-5}{3}). Therefore, the constant of variation is (\frac{-5}{3}).

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