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Algebra / Linear equations in two variables Difficulty: Hard

Line $l$ in the xy-plane is perpendicular to the line with equation $x equals 2$ . What is the slope of line $l$ ?

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Explanation

Choice A is correct. It is given that line $l$ is perpendicular to a line whose equation is x = 2. A line whose equation is a constant value of x is vertical, so $l$ must therefore be horizontal. Horizontal lines have a slope of 0, so $l$ has a slope of 0.

Choice B is incorrect. A line with slope $negative one half$ is perpendicular to a line with slope 2. However, the line with equation x = 2 is vertical and has undefined slope (not slope of 2). Choice C is incorrect. A line with slope –2 is perpendicular to a line with slope $one half$ . However, the line with equation x = 2 has undefined slope (not slope of $one half$ ). Choice D is incorrect; this is the slope of the line x = 2 itself, not the slope of a line perpendicular to it.