the slope formula with two points is
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]where (x2,y2) is the rightmost point between them and (x1,y1) the other point
in this case (x2,y2)=(9,1)
so
[tex]\begin{gathered} m=\frac{1-6}{9-(-6)} \\ m=\frac{-5}{9+6} \\ m=\frac{-5}{15} \\ m=\frac{-1}{3} \end{gathered}[/tex]to find the slope of a perpendicular line you just change the sign of the slope and you reverse the number
so the slop of the perpendicular line is
[tex]m=3[/tex]