Final answer:
To determine whether each pair of lines is perpendicular, parallel, or neither, we compare their slopes. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals, the lines are perpendicular. If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
Step-by-step explanation:
To determine whether each pair of lines is perpendicular, parallel, or neither, we need to compare the slopes of the lines. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular. If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
For the given pairs of lines:
y = 2x + 4 and 2y = 4x - 7
The slopes of both lines are 2, so the lines are parallel.
4y = 2x - 4 and y = -2x + 9
The slopes of both lines are -½, which are negative reciprocals of each other, so the lines are perpendicular.
2y = 4x + 4 and y = -2x + 4
The slopes of the lines are 2 and -2, which are neither equal nor negative reciprocals, so the lines are neither parallel nor perpendicular.