Final answer:
The slope of line r which is perpendicular to line p with the equation 2y+18x=9 is 1/9, option C).
Step-by-step explanation:
The student's question relates to finding the slope of a line that is perpendicular to a given line in the xy-plane.
The equation of line p is 2y+18x=9, which can be rewritten in slope-intercept form (y=mx+b) as y=-9x+4.5, giving us a slope (m) of -9 for line p.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. Therefore, the slope of line r would be the negative reciprocal of -9, which is 1/9.
Thus, the correct answer is C) 1/9.