The lines 2 x - 3 y = 6 and k x + y = 4 are perpendicular. What is the value of k?
Show answer & explanation
Correct answer: D
Explanation
First line: 2x − 3y = 6 ⇒ y = (2/3)x − 2
⇒ m₁ = 2/3
Second line: kx + y = 4 ⇒ y = −kx + 4
⇒ m₂ = −k
⇒ m₁ × m₂ = (2/3)(−k) = −1
⇒ −2k/3 = −1
⇒ 2k/3 = 1
⇒ k = 3/2