In a direct variation, \( y \) varies directly with \( x \) and can be expressed in the form \( y = kx \), where \( k \) is the constant of variation.
Given the equation \( 3x + 5y = 0 \), we can rearrange it to find a relationship between \( x \) and \( y \).
- Isolate \( y \): \[ 5y = -3x \] \[ y = -\frac{3}{5}x \]
From this equation, we can see that \( k = -\frac{3}{5} \).
Thus, the constant of variation \( k \) is: \[ k = -\frac{3}{5} \]
If you'd like to express \( k \) repeatedly as your prompt suggests:
- \( k = -\frac{3}{5} \)
- \( k = -\frac{3}{5} \)
- \( k = -\frac{3}{5} \)
And not equal to 5, as stated at the end of your prompt. The correct value for \( k \) is indeed \( -\frac{3}{5} \).