If w varies directly as z and w = 9 when z = -6, find w when z = 3.

a) 0
b) -4.5
c) -2
d) 4.5

w = kz

so, w/z = k, a constant. So, you want w such that

w/3 = 9/-6

To find the value of w when z = 3, we can use the direct variation formula:

w = k * z

where k is the constant of variation. To determine the value of k, we can use the given information that w = 9 when z = -6:

9 = k * (-6)

To solve for k, divide both sides of the equation by -6:

k = 9 / -6
k = -1.5

Now that we have the value of k, we can substitute it into the direct variation formula to find w when z = 3:

w = -1.5 * 3
w = -4.5

Therefore, the answer is:

b) -4.5