Final answer:
The equations y = -3x and y = -6 have slopes of -3 and 0, respectively, so they are neither parallel nor perpendicular to one another.
Step-by-step explanation:
To determine if the equations y = -3x and y = -6 are parallel, perpendicular, or neither, we first need to examine their slopes. For two lines to be parallel, their slopes must be equal. For two lines to be perpendicular, the slope of one line must be the negative reciprocal of the slope of the other line.
The equation y = -3x has a slope of -3. It's in the form of y = mx + b, where m is the slope. The equation y = -6 represents a horizontal line where the slope is 0, because the value of y is constant and does not depend on x.
Since the slopes of these two lines are -3 and 0, they are neither parallel nor perpendicular. A slope of -3 is not equal to 0 (so not parallel), and the negative reciprocal of -3 is 1/3, which is not 0 (so not perpendicular).