Answer
$y=-3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Point-Slope Form with the given point $(2,-3)$ and the slope perpendicular to $x=2.$
$\bf{\text{Solution Details:}}$
The equation $x=2$ defines a vertical line. Perpendicular to a vertical line is a horizontal line. All horizontal lines have a slope of $0.$ Hence, the needed line has the following characteristics:
\begin{array}{l}\require{cancel}
\text{Slope: }m=0
\\\text{Through: }(2,-3)
.\end{array}
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions,
\begin{array}{l}\require{cancel}
y_1=-3
,\\x_1=2
,\\m=0
,\end{array}
is
\begin{array}{l}\require{cancel}
y-(-3)=0(x-2)
\\\\
y+3=0
\\\\
y=-3
.\end{array}
