sat-dog

Choice C is correct. It's given that when line $n$ is graphed in the xy-plane, it has an x-intercept of $\left(-4,0\right)$ and a y-intercept of $\left(0,\frac{86}{3}\right)$. The slope, $m$, of a line can be found using any two points on the line, $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, and the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Substituting the points $\left(-4,0\right)$ and $\left(0,\frac{86}{3}\right)$ for $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, respectively, in the slope formula yields $m=\frac{{\displaystyle \frac{86}{3}}-0}{0-\left(-4\right)}$, or $m=\frac{43}{6}$. Therefore, the slope of line $n$ is $\frac{43}{6}$.

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

Choice B is incorrect. This is the slope of a line that has an x-intercept of $\left(\frac{86}{3},0\right)$ and a y-intercept of $\left(0,-4\right)$.

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