To determine if the lines represented by the equations x = 1 and y = -8 are parallel, perpendicular, or neither, we need to examine their slopes.
The equation x = 1 represents a vertical line that passes through the point (1, 0). Vertical lines have an undefined slope because their rise (change in y) is always 0, while their run (change in x) can be any value.
The equation y = -8 represents a horizontal line that passes through the point (0, -8). Horizontal lines have a slope of 0 because their rise is always 0, while their run can be any value.
Since the slope of the vertical line x = 1 is undefined and the slope of the horizontal line y = -8 is 0, these lines are neither parallel nor perpendicular.
Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. In this case, the slopes are neither the same nor negative reciprocals, indicating that the lines are neither parallel nor perpendicular.