Question

8.
Find the constant of variation k for the direct variation.

3x + 5y = 0

Answer 1

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

We start with the equation given:

\[
3x + 5y = 0
\]

To express \( y \) in terms of \( x \), we can rearrange the equation:

\[
5y = -3x
\]

Now, divide both sides by 5:

\[
y = -\frac{3}{5}x
\]

Here, we can see that this equation is in the form \( y = kx \), where \( k = -\frac{3}{5} \).

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

\[
\boxed{-\frac{3}{5}}.
\]