To solve the exercise you can use the point-slope formula, that is,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} m=-\frac{5}{6} \\ (x_1,y_1)=(8,-4) \end{gathered}[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-4)_{}=-\frac{5}{6}(x-8) \\ y+4_{}=-\frac{5}{6}(x-8) \end{gathered}[/tex]Therefore, the equation in point-slope form for the given point and slope is
[tex]y+4_{}=-\frac{5}{6}(x-8)[/tex]and the correct answer is C.
