Line k is defined by y = 7 x + 1 8 . Line j is

Choice B is correct. It's given that line $k$ is defined by $y=7x+\frac{1}{8}$. For an equation in slope-intercept form $y=mx+b$, $m$ 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 $k$.