Line L has equation y = 2x + 3, and line M has the same y-intercept as L Which of the points below must M contain to be perpendicular to L, is

Question

Line L has equation y = 2x + 3, and line M has the same y-intercept as L Which of the points below must M contain to be perpendicular to L, is (A) (- 4, 5) (B) (- 2, 5) (C) (1, 5) (D) (4, 5)

Tardigrade Admin · Accepted Answer

y-intercept of M is 3 ⇒ line M passes through (0,3); slope of M =(-1/2) Equation of M is y-3=(-1/2)(x-0) ⇒ 2 y-6=-x ⇒ x+2 y=6 ⇒ (A) satisfies it.

Q. Line L has equation $y = 2 x + 3$ , and line $M$ has the same y-intercept as $L$ Which of the points below must $M$ contain to be perpendicular to $L$ , is

(- 4, 5)

(- 2, 5)

(1, 5)

(4, 5)

$y$ -intercept of $M$ is $3 \Rightarrow$ line $M$ passes through $(0, 3)$ ; slope of $M = \frac{- 1}{2}$
Equation of $M$ is $y - 3 = \frac{- 1}{2} (x - 0) \Rightarrow 2 y - 6 = - x$
$\Rightarrow x + 2 y = 6 \Rightarrow$ (A) satisfies it.

Q. Line L has equation y=2x+3, and line M has the same y-intercept as L Which of the points below must M contain to be perpendicular to L, is