Final answer:
The two lines represented by y = -6x + 3 and y = (1/-6)x - 4 are perpendicular to each other because their slopes are negative reciprocals of each other.
Step-by-step explanation:
To determine whether the given lines are parallel, perpendicular, or neither, we need to compare their slopes. The equations given are y = -6x + 3 and y = \(\frac{1}{-6}\)x - 4. The slope of a line in slope-intercept form (y = mx + b) is the coefficient of x, which is the 'm' value. In the first equation, the slope is -6, and in the second equation, the slope is -\(\frac{1}{6}\). Since the slopes are negative reciprocals of each other, the lines are perpendicular to each other. If two lines are perpendicular, their slopes are negative reciprocals (the product of their slopes is -1).