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  4. 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

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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

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Solution:

$y$-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.