In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

Line $x=-5$, Point$(2,1)$

Line $x=-5$,

Point $(2,1)$.

We have to find the equation of line perpendicular to the line $x=-5$and also passing through the point $(2,1)$.

Slopes of perpendicular lines are negative reciprocals to each other.

That is $m_2=-\frac{1}{m_1}$, where, $m_1,m_2$are slopes of the two perpendicular lines.

The given line $x=-5$is a vertical line.

So the slope of the line is not defined.

The given line is a vertical line with an undefined slope.

A line perpendicular to a vertical line will be a horizontal line.

The slope of a horizontal line is $0$.

The general equation of a horizontal line is of the form $y=k$.

Where $k$is constant.

The required line contains the point $(2,1)$, so the line equation is $y=1$.

Therefore the slope-intercept form of the line that is perpendicular to $x=-5$and contains the point $(2,1)$is $y=1$.