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

To find the constant of variation \( k \) in the equation \( y = kx \) using the point \((-3, 2)\), you can substitute the coordinates into the equation. This gives you \( 2 = k(-3) \). Solving for \( k \), you divide both sides by \(-3\), resulting in \( k = \frac{2}{-3} = -\frac{2}{3} \). Now, for direct variation, remember that the value of \( k \) determines the steepness and direction of the line. If \( k \) is positive, the line rises to the right, and if negative, it falls. Here, since \( k = -\frac{2}{3} \), the graph of the function will slope downwards as \( x \) increases.