Does the equation 3 x + 5 y = 0 represent a direct variation and...

The constant of variation is ${\displaystyle \frac{3}{5}}$
I'll let you decide whether this is a good or bad thing.
Explanation:
We have: ${\displaystyle 3x+5y=0}$
Subtract 3x from both sides
${\displaystyle 3x-3x+5y=0-3x}$
0+5y=-3x
${\displaystyle 5y=-3x}$
Divide both sides by 5
${\displaystyle \frac{5}{5}\times y=-\frac{3}{5}x}$
But ${\displaystyle \frac{5}{5}=1}$
${\displaystyle y=-\frac{3}{5}x}$
If you wish the x to be positive: multiply both sides by (-1)
${\displaystyle -y=+\frac{3}{5}x}$
The constant of variation is ${\displaystyle \frac{3}{5}}$