Final answer:
The equation of a line perpendicular to the vertical line x=-5 and passing through the point (2, -9) is y=-9. This is because the perpendicular line must be horizontal, which has an equation y=k, where k is the y-coordinate of any point on the line.
Step-by-step explanation:
To find an equation of a line perpendicular to x= -5 and passing through the point (2, -9), we need to understand the characteristics of perpendicular lines in the coordinate system. The line x= -5 is a vertical line, which means any line perpendicular to it will be a horizontal line. Horizontal lines have equations of the form y = k, where k is a constant value representing the y-coordinate of every point on the line.
Our line needs to pass through the point (2, -9). Since our line is horizontal, the y-value for all points on the line must be the same as the y-coordinate of this point. Therefore, the equation of our line is simply y = -9.
This result is independent of the x-coordinate of the point through which the line passes. This is because the slope of the line is 0, and only the y-coordinate affects the equation of a horizontal line. There is no need to identify components or use trigonometry because we are dealing with a special case of horizontal and vertical lines where their perpendicular counterparts have a slope of either 0 (horizontal line) or undefined (vertical line).