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Algebra Difficulty: Medium

Line $k$ is defined by $y = 7 x + \frac{1}{8}$ . Line $j$ is perpendicular to line $k$ in the xy-plane. What is the slope of line $j$ ?

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Explanation

Choice B is correct. It's given that line $k$ is defined by $y = 7 x + \frac{1}{8}$ . For an equation in slope-intercept form $y = m x + b$ , $m$ represents the slope of the line defined by this equation in the xy-plane and $b$ represents the y-coordinate of the y-intercept of this line. Therefore, the slope of line $k$ is $7$ . It’s also given that line $j$ is perpendicular to line $k$ in the xy-plane. Therefore, the slope of line $j$ is the opposite reciprocal of the slope of line $k$ . The opposite reciprocal of $7$ is $- \frac{1}{7}$ . Therefore, the slope of line $j$ is $- \frac{1}{7}$ .

Choice A is incorrect. This is the opposite reciprocal of the y-coordinate of the y-intercept, not the slope, of line $k$ .

Choice C is incorrect. This is the y-coordinate of the y-intercept of line $k$ , not the slope of line $j$ .

Choice D is incorrect. This is the slope of a line that is parallel, not perpendicular, to line $k$ .