Question

2.
Find the constant of variation k for the direct variation.

4x = –6y

Answer 1

In a direct variation, the relationship between \( x \) and \( y \) can be expressed as:

\[
y = kx
\]

where \( k \) is the constant of variation.

From the equation \( 4x = -6y \), we can rearrange it to find the relationship between \( x \) and \( y \):

\[
-6y = 4x
\]

Dividing both sides by -6 gives:

\[
y = -\frac{4}{6}x
\]

Simplifying \(-\frac{4}{6}\):

\[
y = -\frac{2}{3}x
\]

Now, comparing this to the direct variation formula \( y = kx \), we can see that the constant of variation \( k \) is:

\[
k = -\frac{2}{3}
\]

Thus, the constant of variation \( k \) is \(-\frac{2}{3}\).