Answer:
x - 3y = 6 and x - 3y = 9 ⇒ Parallel
y = 4x + 1 and y = -4x - 2 ⇒ Neither
Explanation:
Parallel lines have the same slope. Given the definition of parallel lines, it is easier to tell that the graph of x - 3y = 6 and x - 3y = 9 will have parallel lines, since both equations have the same slope of -1/3.
Perpendicular lines have negative reciprocal slopes. This means that if you multiply the slopes of both equations, it will result with a product of -1. Another important aspect of perpendicular lines is that they have a single point of intersection, and that they intersect at a 90° angle.
The graph of equations y = 4x + 1 and y = -4x - 2 intersect, but are not perpendicular from each other because they do not have negative reciprocal slopes. The negative reciprocal slope of 4 is -¼; likewise, the negative reciprocal slope of -4 is ¼.
Therefore, the graph of y = 4x + 1 and y = -4x - 2 are neither parallel or perpendicular.