Question

6.
Find the constant of variation k for the direct variation.

2x + 6y = 0

Answer 1

To find the constant of variation \( k \) for the direct variation given by the equation \( 2x + 6y = 0 \), we can first rearrange this equation into a form that highlights the relationship between \( x \) and \( y \).

Start by isolating \( y \):

\[
6y = -2x
\]

Now, divide both sides by 6:

\[
y = -\frac{2}{6}x
\]

Simplifying \(-\frac{2}{6}\):

\[
y = -\frac{1}{3}x
\]

In the context of direct variation, this can be expressed in the form \( y = kx \), where \( k \) is the constant of variation. Here, we can see that:

\[
k = -\frac{1}{3}
\]

Thus, the constant of variation \( k \) is:

\[
\boxed{-\frac{1}{3}}
\]