The graph of a linear function z is shown below.

To determine the slope of the linear function from the given points, we can use the formula for slope:

m = (y2 - y1) / (x2 - x1)

Using the points (-2, 6) and (5, -4.5):

m = (-4.5 - 6) / (5 - (-2))
m = (-10.5) / 7
m = -1.5

Therefore, the slope of the linear function z is -3/2.

So the correct answer is C. -3/2.