Final answer:
The equations Y = 4x + 1 and y = -4x + 2 are perpendicular because their slopes are negative reciprocals of each other (4 and -4, respectively).
Step-by-step explanation:
To determine whether the equations Y = 4x + 1 and y = -4x + 2 are perpendicular, parallel, or neither, we need to look at their slopes. If two lines are perpendicular, their slopes are negative reciprocals of each other. This means that if one line has a slope of 'm', the other must have a slope of '-1/m'. In the case of parallel lines, they would have the exact same slope.
The slope of Y = 4x + 1 is 4, and the slope of y = -4x + 2 is -4. Since 4 and -4 are negative reciprocals of each other (4 = -1/(-1/4)), the two lines are perpendicular to each other.
Therefore, the correct answer is option 1) Perpendicular.