Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.Application

The correct answer is: ∴ Equation of the given line is y = -9.

Step-by-step solution:-
Let l be the line for which slope is to be found.
The given equation of line x = 5 represents a verticle line (because its y-coordinate = 0)
Now, line l is perpendicular to the given line (x = 5).
∴ line l is a horizontal line i.e. parallel to x-axis.
Slope of a horizontal line i.e. parallel to x-axis is always 0
∴ Slope of line l = m = 0 …...................................................................................................... (Equation i)
We are given that line l passes through the point (2,-9) and we know its slope.
i.e. x1 = 2 & y1 = -9 & m = 0
We can use slope point form of an equation to find the equation of line l-
(y - y1) = m (x-x1)
∴ [y - (-9)] = 0 (x-2)
∴ y + 9 = 0
∴ y = -9