Question

what is the slope of a line perpendicular to the line that contains the points (9,1) and (-6,6)

Answer 1

the slope formula with two points is

$m=\frac{y_2-y_1}{x_2-x_1_{}}$

where (x2,y2) is the rightmost point between them and (x1,y1) the other point

in this case (x2,y2)=(9,1)

so

$\begin{gathered} m=\frac{1-6}{9-(-6)} \\ m=\frac{-5}{9+6} \\ m=\frac{-5}{15} \\ m=\frac{-1}{3} \end{gathered}$

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

$m=3$