Question

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

Answer 1

q = 1.

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.