Since we know it is perpendicular to [tex]y=3x-9[/tex], we know the slope of the line is the opposite reciprocal of 3, or [tex]-\frac{1}{3}[/tex]. Then we can use the two points in the slope formula to solve for k:
[tex]-\frac{1}{3}=\frac{5-1}{k-2}[/tex]
[tex]-\frac{k-2}{3}=4[/tex]
[tex]k-2=-12[/tex]
[tex]k=-10[/tex]
