The line x = 0 is perpendicular to the line y = -3:
Correct. Any horizontal line (y = a) and any vertical line (x = b) intersect at some point and are perpendicular.
All lines that are parallel to the y-axis are vertical lines:
Correct. The y-axis is a vertical line, so any lines that are parallel to it must also be vertical.
All lines that are perpendicular to the x-axis have a slope of 0.
Incorrect. Lines that have a slope of 0 are horizontal, and the x-axis is horizontal as well. Any lines with a slope of 0 are parallel to the x-axis, not perpendicular to it.
The equation of the line parallel to the x-axis that passes through the point (2, 6) is x = 2.
Incorrect. x = 2 is a vertical line, and vertical lines cannot be parallel to the horizontal x-axis. x = 2 is perpendicular to the x-axis, however.
The equation of the line perpendicular to the y-axis that passes through the point (-5, 1) is y = 1.
Correct. The line y = 1 is horizontal, and the y-axis is a vertical line. Because the line y = 1 crosses the y-axis, the lines are perpendicular.
