To find the equation of a line, we use the slope-intercept from formula shown below:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]We just need 2 points from the line. They are:
[tex]\begin{gathered} (x_1,y_1)=(5,-6) \\ \text{and} \\ (x_2,y_2)=(-3,-4) \end{gathered}[/tex]Substituting, we get:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}_{}(x-x_1) \\ y-(-6)=\frac{-4-(-6)_{}}{-3-5}(x-5)_{} \\ y+6=\frac{-4+6}{-8}(x-5) \\ y+6=\frac{2}{-8}(x-5) \\ y+6=-\frac{1}{4}(x-5) \\ y+6=-\frac{1}{4}x+\frac{5}{4} \\ y=-\frac{1}{4}x+\frac{5}{4}-6 \\ y=-\frac{1}{4}x-\frac{19}{4} \end{gathered}[/tex]