Question

Find the value of K so that the lines x-2y=3, kx+3y=1 would be parallel.

Answer 1

Re-arrange in the form y = mx + c :

x - 2y = 3 ⇒ 2y = x - 3 ⇒ y = 0.5x - 3/2 ⇒ Gradient = 1/2.

kx + 3y = 1 ⇒ 3y = -kx + 1 ⇒ y = -kx/3 + 1/3 ⇒ Gradient = -k/3.

Parallel lines have the same gradient so:

-k/3 = 1/2

⇒ -k = 3/2

⇒ k = -3/2.