To find the constant of variation [tex]\( k \)[/tex] for the direct variation equation [tex]\( y = kx \)[/tex] that passes through the point [tex]\((-3, 2)\)[/tex], we follow these steps:
1. Identify the given point:
- The given point is [tex]\((-3, 2)\)[/tex].
- This means when [tex]\( x = -3 \)[/tex], [tex]\( y = 2 \)[/tex].
2. Recall the direct variation formula:
- The formula for direct variation is [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of variation.
3. Substitute the values into the formula:
- Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 2 \)[/tex] into the equation [tex]\( y = kx \)[/tex]:
[tex]\[
2 = k \cdot (-3)
\][/tex]
4. Solve for [tex]\( k \)[/tex]:
- Rearrange the equation to solve for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{y}{x} = \frac{2}{-3}
\][/tex]
Therefore, the constant of variation [tex]\( k \)[/tex] is:
[tex]\[
k = -\frac{2}{3}
\][/tex]
This value corresponds to one of the provided choices. So, the correct answer is:
[tex]\[ k = -\frac{2}{3} \][/tex]
