To determine the constant of variation, [tex]\( k \)[/tex], for the direct variation equation [tex]\( y = kx \)[/tex] given the point [tex]\((-3, 2)\)[/tex], follow these steps:
1. Start with the direct variation equation:
[tex]\[
y = kx
\][/tex]
2. Substitute the given point [tex]\((-3, 2)\)[/tex] into the equation:
[tex]\[
2 = k(-3)
\][/tex]
3. Solve for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{2}{-3} = -\frac{2}{3}
\][/tex]
Therefore, the constant of variation [tex]\( k \)[/tex] is [tex]\(-\frac{2}{3}\)[/tex].
The correct answer is:
[tex]\( k = -\frac{2}{3} \)[/tex]
