What is the constant of variation k in the direct variation equation y = kx when the coordinates are (3, 2)?

To determine the constant of variation k in the direct variation equation of the form y = kx, we need to use the coordinates provided.

Given the point (3, 2), we can interpret this as x = 3 and y = 2. We can substitute these values into the equation:

y = kx

This leads to:

2 = k(3)

To solve for k, we simply divide both sides of the equation by 3, as follows:

k = 2 / 3

Thus, the constant of variation k is:

k = rac{2}{3}

In conclusion, in the direct variation equation y = kx that passes through the point (3, 2), the constant of variation is k = rac{2}{3}.