SAT Question 265f2a53: Linear Equations In Two Variables answer and explanation with Desmos solution

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 $m=\frac{\frac{86}{3}-0}{0-\left(-4\right)}$, or $m=\frac{43}{6}$. Therefore, the slope of line $n$ is $\frac{43}{6}$.