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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.