Question

Find the constant of variation k for the direct variation.

4x = –6y



k =


k = –6


k =


k =

Answer 1

In a direct variation, the relationship between two variables can be expressed in the form \( y = kx \), where \( k \) is the constant of variation.

Given the equation \( 4x = -6y \), we can rearrange it to find \( k \).

1. First, solve for \( y \):
\[
-6y = 4x
\]
\[
y = -\frac{4}{6}x
\]
\[
y = -\frac{2}{3}x
\]

2. Here, we can see that the constant of variation \( k \) is \(-\frac{2}{3}\).

Therefore, we conclude:
\[
k = -\frac{2}{3}
\]