Answer:
[tex]k=-\frac{1}{3}[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have
[tex]2x+6y=0[/tex]
Isolate the variable y
subtract 2x both sides
[tex]2x+6y-2x=0-2x[/tex]
[tex]6y=-2x[/tex]
Divide by 6 both sides
[tex]y=-\frac{1}{3}x[/tex]
therefore
The constant of variation is equal to
[tex]k=-\frac{1}{3}[/tex]
