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{1}{4} \\ (x_1,y_1)=(-4,8) \end{gathered}[/tex][tex]\begin{gathered} y-8=\frac{-1}{4}(x-(-4)) \\ y-8=\frac{-1}{4}(x+4) \\ y-8=\frac{-1}{4}\cdot x-\frac{1}{4}\cdot4 \\ y-8=\frac{-1}{4}x-1 \\ \text{ Add 8 to both sides of the equation} \\ y-8+8=\frac{-1}{4}x-1+8 \\ y=\frac{-1}{4}x+7 \end{gathered}[/tex]Therefore, the equation of the line that passes through the point (-4, 8) and has a slope of -1/4 is
[tex]y=\frac{-1}{4}x+7[/tex]
