The correct answer is $\dfrac{3}{17}$ . It’s given that line $j$ is perpendicular to line $k$ in the $xy$-plane. This means that the slope of line $j$ is the negative reciprocal of the slope of line $k$. The equation of like $k$,$y=\dfrac{-17}{3}x+5$, 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 $\dfrac{-17}{3}$. The negative reciprocal of a number is $-1$ divided by the number. Therefore, the negative reciprocal of $\dfrac{-17}{3}$ is $\dfrac{-1}{\dfrac{-17}{3}}$, or $\dfrac{3}{17}$. Thus, the slope of line $j$ is $\dfrac{3}{17}$.

Note that $3/17$ , $.1764$, $.1765$, and $0.176$ are examples of ways to enter a correct answer.