Perpendicular lines: The slope is the opposite reciprocal. For example, a line perpendicular to a slope of 3x would be -1/3x.

Parallel lines: The slopes are the same. A line parallel to a slope of 5x would be 5x.

Y=4x+5 and Y=-1/4x+4 are perpendicular to eachother, because the slope of line one is 4x. Opposite of 4? -4. Reciprocal? -1/4.

The lines are perpendicular to eachother.

It's perpendicular, since the slopes are negative reciprocals. First one is 4/1 and second one is -1/4 they just flipped it, when the slopes are flipped its perpendicular. So it's different, parallel would be the same slope. So 4x and 4x are parallel.