Question

Find the constant of variation k for the direct variation. 2x + 6y = 0

Answer 1

Answer:

$k=-\frac{1}{3}$

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 $k=\frac{y}{x}$ or $y=kx$

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

$2x+6y=0$

Isolate the variable y

subtract 2x both sides

$2x+6y-2x=0-2x$

$6y=-2x$

Divide by 6 both sides

$y=-\frac{1}{3}x$

therefore

The constant of variation is equal to

$k=-\frac{1}{3}$