Question

What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)?

k = –k equals negative StartFraction 3 Over 2 EndFraction.
k = –k equals StartFraction 2 Over 3 EndFraction.
k = k equals StartFraction 2 Over 3 EndFraction.
k = k equals StartFraction 3 Over 2 EndFraction.

Answer 1

In a direct variation represented by the equation \( y = kx \), we can find the constant of variation \( k \) by substituting the coordinates of the point (–3, 2) into the equation.

Given:
- \( x = -3 \)
- \( y = 2 \)

Substituting these values into the equation:

\[
2 = k(-3)
\]

To solve for \( k \), we can rearrange the equation:

\[
k = \frac{2}{-3} = -\frac{2}{3}
\]

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

\[
k = -\frac{2}{3}
\]

Therefore, the correct choice is:
\[
k = -\frac{2}{3}
\]