Answer :
When a line is given in the form
[tex]y=mx+q[/tex]
The slope of the line is m. So, in this case, the slope of [tex]y=-x-11[/tex] is -1.
Given a slope [tex]m[/tex], you find the slope of a perpendicular line [tex]m'[/tex] by imposing
[tex]m\cdot m' = -1[/tex]
So, if the given line has slope -1, a perpendicular line has slope [tex]m'[/tex] given by
[tex]-1 \cdot m' = -1[/tex]
and thus [tex]m'=1[/tex]
So, we want a line with slope 1 and passing through (9,2). Using the fomula
[tex]y-y_0=m(x-x_0)[/tex]
we get
[tex]y-2=1(x-9) \iff y-2=x-9 \iff y=x-7[/tex]