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 $y=mx+b$, 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 $-1$ divided by the number. Thus, the opposite reciprocal of $3$ is $\dfrac{-1}{3}$. Therefore, the slope of line $j$ is $\dfrac{-1}{3}$.

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.