In a direct variation described by the equation [tex]\( y = kx \)[/tex], [tex]\( k \)[/tex] is known as the constant of variation. To find the constant of variation for the point [tex]\((-3, 2)\)[/tex], we need to determine the value of [tex]\( k \)[/tex] that satisfies the equation when [tex]\( x = -3 \)[/tex] and [tex]\( y = 2 \)[/tex].
Given the equation [tex]\( y = kx \)[/tex]:
1. Substitute the coordinates [tex]\((-3, 2)\)[/tex] into the equation.
[tex]\[
2 = k(-3)
\][/tex]
2. Solve for [tex]\( k \)[/tex] by isolating [tex]\( k \)[/tex].
[tex]\[
k = \frac{2}{-3}
\][/tex]
Thus, the constant of variation is:
[tex]\[
k = -\frac{2}{3}
\][/tex]
Therefore, the correct answer is:
[tex]\( k = -\frac{2}{3} \)[/tex]
