Final answer:
To find the equation of a line perpendicular to x=-2 and passing through (-6,2), you identify that a line perpendicular to a vertical line is horizontal with a slope of 0. The equation is therefore y=2, a horizontal line passing through the point (-6,2).
Step-by-step explanation:
The student is asking how to find the equation of a line that goes through the point (-6,2) and is perpendicular to the line given by the equation x=-2. In coordinate geometry, when two lines are perpendicular, their slopes are negative reciprocals of one another.
Since the line x=-2 is a vertical line, its slope is undefined, and the perpendicular line to it would be a horizontal line, which has a slope of 0. Therefore, the equation of the line we are looking for will have the form y=k, where k is the y-coordinate of the given point through which the line passes.
To find the value of k, we simply use the y-coordinate of the given point (-6, 2), so our line's equation becomes y=2. This equation represents a horizontal line that passes through (-6, 2) and is perpendicular to the vertical line x=-2.