Final answer:
The equation of the line that is perpendicular to x = -6 and passes through the point (-1, -2) is y = -2, which denotes a horizontal line with a slope of 0.
Step-by-step explanation:
To find the equation of a line that is perpendicular to x = -6 and passes through the point (-1, -2), we need to understand the characteristics of perpendicular lines.
The line x = -6 is a vertical line, so a line perpendicular to it would be a horizontal line.
Horizontal lines have a slope of 0.
Therefore, the equation of our line will not change in the y-value as x changes.
The equation for any horizontal line can be written as y = k, where k is the y-coordinate of any point the line passes through.
As the line passes through the point (-1, -2), we take the y-coordinate from this point, which is -2.
So the equation for the line that is perpendicular to x = -6 and passes through (-1, -2) is y = -2.