Is 2x plus 3y equals 0 a direct variation?

Answer 1

Direct variation refers to two variable quantities have a constant (unchanged) ratio, in which a variable "varies directly with the other."

In order to have a direct variation, the constant of variation must be not equal to 0 in the equation y=kx, where k is the constant.

When you try to put 2x+3y=0 into that formula (y= form), you get:

2x+3y=0

3y=-2x ;Subtract the 2x

y=(-2/3)x ;Divide by 3

Your constant of variation is -2/3, and since it is less than 0, it is does variate directly. Therefore, y varies directly as x.