"Recall that if two lines are perpendicular to each other then"
"their slopes are negative reciprocals of each other or one is"
"vertical (having no slope) and the other is horizontal (having"
"zero slope)."
"Our line" \ q, "has slope 2, and so is neither vertical nor horizontal."
"So, any line perpendicular to" \ q \ "has slope that is the negative"
"reciprocal of the slope of line" \ q.
"So let" \ p \ "be a line perpendicular to line" \ q.
"Then we have:"
\qquad \qquad \quad "slope of" \ p \ = \ "negative reciprocal of slope of line" \ q
\qquad \qquad \qquad \qquad \qquad \qquad \quad \ = \ "negative reciprocal of" \ (2)
\qquad \qquad \qquad \qquad \qquad \qquad \quad \ = \ "negative of" \ (1/2)
\qquad \qquad \qquad \qquad \qquad \qquad \quad \ = \ -1/2.
"Thus:"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad "slope of" \ p \ = \ -1/2.
"So:"
\qquad \qquad \qquad "slope of any line perpendicular to" \ q \ = \ -1/2.
"This is our answer."