write the equation of a line that is perpendicular to x=2 and goes through the point (-6,3)

Answer 1

x=2 is a vertical line at the numerical value 2 on the x axis.

This means a perpendicular line to x=2 would need to be a horizontal line, written in the format of y=?

Since you are asked for a line which passes through the point (-6,3), which tells you that x=-6 and y=3, the equation for your line is simply y=3

(This may be easier to visualize drawn on a graph!)

Answer 2

x = 2 (graph it!) is a vertical line.

The line perpendicular is a horizontal line

Horisontal lines are in the form y = k.

In this case y = 3 (graph it and see!)