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Algebra / Linear equations in two variables Difficulty: Easy

Line $k$ is defined by $y = 3 x + 15$ . Line $j$ is perpendicular to line $k$ in the xy-plane. What is the slope of line $j$ ?

$- \frac{1}{3}$

$- \frac{1}{12}$

$- \frac{1}{18}$

$- \frac{1}{45}$

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Explanation

Choice A is correct. It's given that line $j$ is perpendicular to line $k$ in the xy-plane. It follows that the slope of line $j$ is the opposite reciprocal of the slope of line $k$ . The equation for line $k$ is written in slope-intercept form $y = m x + b$ , where $m$ is the slope of the line and $b$ is the y-coordinate of the y-intercept of the line. It follows that the slope of line $k$ is $3$ . The opposite reciprocal of a number is $negative 1$ divided by the number. Thus, the opposite reciprocal of $3$ is $- \frac{1}{3}$ . Therefore, the slope of line $j$ is $- \frac{1}{3}$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.