Final answer:
Option A. The equation of a vertical line passing through the point (-5,6) is x = -5. This is because a vertical line intersects the x-axis at a specific point, and all points on the line share the same x-coordinate.
Step-by-step explanation:
To find the equation of a vertical line passing through the point (-5,6), we should recall the nature of vertical lines in a coordinate plane. A vertical line has an undefined slope and it intersects the x-axis at a particular point. In this case, the line passes through x = -5, which means every point on this line has an x-coordinate of -5. Therefore, the equation representing this vertical line is x = -5.
Option b) y = 6 would represent a horizontal line that intersects the y-axis at the point (0,6), which is not the type of line we're looking for. Similarly, options c) y = -5x + 6 and d) x = 6 don't represent a vertical line at x = -5 either. Option c) is a line with a negative slope and option d) represents a vertical line intersecting the x-axis at (6,0).
Hence, the correct answer is a) x = -5, which defines the vertical line passing through the point (-5,6).