Question

what is the constant of variation, k, of the direct variation, y = kx, through (-3, 2)?
\\( k = \frac{3}{2} \\)
\\( k = \frac{2}{3} \\)
\\( k = \frac{2}{3} \\)
\\( k = \frac{3}{2} \\)

Explanation:

Step1: Substitute the point into the equation

We know the direct variation equation is \( y = kx \), and the point \((-3, 2)\) lies on this line. So we substitute \( x=-3 \) and \( y = 2 \) into the equation.
\( 2=k\times(-3) \)

Step2: Solve for \( k \)

To find \( k \), we divide both sides of the equation \( 2=-3k \) by \(-3\).
\( k=\frac{2}{-3}=-\frac{2}{3} \)

Answer:

\( k = -\frac{2}{3} \) (corresponding to the option \( k = -\frac{2}{3} \))