Answer
$y=2x-7$, or, in general form, $2x-y-7=0$
Work Step by Step
Through $(-2,-11);$ perpendicular to the line passing through $(1,1)$ and $(5,-1)$
A point through which the line passes and the fact that the line whose equation must be found is perpendicular to the line passing through $(1,1)$ and $(5,-1)$ are known.
Use the point-slope form of the equation of a line, which is $y-y_{1}=m(x-x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is the slope.
Two points through which the line perpendicular to the one whose equation must be found passes are known. Use them to find its slope:
$m_{\perp}=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}=\dfrac{-1-1}{5-1}=\dfrac{-2}{4}=-\dfrac{1}{2}$
The slopes of perpendicular lines are negative reciprocals, so the slope of the line whose equation must be found is:
$m=-\dfrac{1}{\Big(-\dfrac{1}{2}\Big)}=2$
Substitute $(x_{1},y_{1})$ and $m$ into the point-slope form of the equation of a line formula and simplify to obtain the answer:
$y-y_{1}=m(x-x_{1})$
$y+11=2(x+2)$
$y+11=2x+4$
$y=2x+4-11$
$y=2x-7$, or, in general form, $2x-y-7=0$
