Linear equations in two variables SAT question

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

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