Line k is defined by y = - 17 3 x + 5 . Line j

The correct answer is $\frac{3}{17}$. 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 line $k$, $y=-\frac{17}{3}x+5$, 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 $-\frac{17}{3}$. The negative reciprocal of a number is $-1$ divided by the number. Therefore, the negative reciprocal of $-\frac{17}{3}$ is $\frac{-1}{-{\displaystyle \frac{17}{3}}}$, or $\frac{3}{17}$. Thus, the slope of line $j$ is $\frac{3}{17}$. Note that 3/17, .1764, .1765, and 0.176 are examples of ways to enter a correct answer.