Question

what is the constant of variation, k, of the direct variation, $y = kx$, through $(-3, 2)$?
$\bigcirc$ $k = -\frac{3}{2}$
$\bigcirc$ $k = -\frac{2}{3}$
$\bigcirc$ $k = \frac{1}{3}$
$\bigcirc$ $k = \frac{3}{2}$

Explanation:

Step1: Substitute point into equation

Substitute $x=-3$, $y=2$ into $y=kx$:
$2 = k\times(-3)$

Step2: Solve for k

Isolate k by dividing both sides by -3:
$k = \frac{2}{-3} = -\frac{2}{3}$

Answer:

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