Question

how do you find the constant of variation k for the direct variation?

for example, 4x + -6y. how do you find k?

Answer 1

If you had
6 y = 4 x
y = (4/6) x
y = (2/3) x

If you had
6 y = -4 x
y = (-2/3) x

Answer 2

Of course direct variation is not always linear.
If 6 y = 4 x^3
then y = (2/3) x^3