The slope of a line is determined by the formula:
(y2 - y1) / (x2 - x1)
So for the points (9, 5) and (21, -5), the slope would be:
(-5 - 5) / (21 - 9) = -10 / 12 = -5/6
So the slope of the line that passes through the points (9, 5) and (21, -5) is -5/6 in simplest form.