Question

What is the value of ab if the lines 2x+ay=6 and by=6x-9 are perpendicular? (I understand they are negative reciprocals, so 'a' times 'b' is -1, just not sure what to do from here)

Answer 1

a y = - 2 x + 6 , y = -2/a x + 6/a
slope1 = -2/a

y = 6/b - 9/b
slope2 = 6/b

slope2 = -1/slope1
6/b = -1/ (-2/a) = 2/a
6 a = 2 b
b = 3 a

a b = 3 a^2

Answer 2

oops.
6/b = -1/ (-2/a) = 2/a
should be
6/b = -1/ (-2/a) = a/2
so ab = 12

Answer 3

Tilt !
Thank you oobleck !