Choice C is correct. It's given that when line $n$ is graphed in the xy-plane, it has an x-intercept of $left parenthesis negative 4 comma 0 right parenthesis$ and a y-intercept of $left parenthesis 0 comma StartFraction 86 Over 3 EndFraction right parenthesis$ . The slope, $m$ , of a line can be found using any two points on the line, $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ , and the slope formula $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ . Substituting the points $left parenthesis negative 4 comma 0 right parenthesis$ and $left parenthesis 0 comma StartFraction 86 Over 3 EndFraction right parenthesis$ for $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ , 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 $StartFraction 43 Over 6 EndFraction$ .

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 $left parenthesis StartFraction 86 Over 3 EndFraction comma 0 right parenthesis$ and a y-intercept of $left parenthesis 0 comma negative 4 right parenthesis$ .

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