Final answer:
The slope of line q, which is perpendicular to line p with a slope of -9/2, is the negative reciprocal of -9/2. Therefore, the slope of line q is 2/9.
Step-by-step explanation:
The equation of the line p is y = -9/2x + 5. To find the slope of line q, which is perpendicular to p, we need to understand the relationship between the slopes of perpendicular lines. In a two-dimensional plane, two non-vertical lines are perpendicular if the product of their slopes is -1. This means that the slope of one line is the negative reciprocal of the slope of the other.
The slope of line p is -9/2. To find the negative reciprocal, we flip the fraction and change the sign, which gives us 2/9. Therefore, the slope of line q is 2/9.