Answer
The equation in slope-intercept form of the line perpendicular to the line $x=6$ and passing through the point $\left( -1,5 \right)$ is $y=5$.
Work Step by Step
The line $x=6$ is the vertical line. Then, this line has undefined slope.
The horizontal line having zero slope is perpendicular to a vertical line having undefined slope.
Thus, the slope of the line perpendicular to the line $x=6$ is 0.
Substitute the value of the slope of the line $m=0$ and point $\left( {{x}_{1}},{{y}_{1}} \right)=\left( -1,5 \right)$ in the equation $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$.
$\begin{align}
& y-5=\left( 0 \right)\left( x-\left( -1 \right) \right) \\
& y-5=0 \\
& y=5
\end{align}$
Thus, the required equation of the line is $y=5$.
