Find q so that the lines y = (1 - 2q) x - 1 and (2 - q) y = x + 5 are perpendicular.

q = 1.

Step-by-step explanation:

y = (1 - 2q) x - 1

The slope of this line is 1 - 2q.

(2 - q) y = x + 5

y = x / (2 - q) + 5 / (2 - q)

The slope of this line is 1 / (2 - q).

When lines are perpendicular the slopes m1 and m2 have the relation

m1. m2 = - 1, so

(1 - 2q) * 1 / (2 - q) = - 1

1 - 2q = - 2 + q

-3q = - 3

q = 1.