Answer: Line A and Line B are not parallel because they have different slopes.
Explanation:
To determine if two lines are parallel, we need to compare their slopes. The slope of a line can be found using the formula:
slope = (change in y-coordinates)/(change in x-coordinates)
For Line A passing through the points (2, -3) and (6, 9):
change in y-coordinates = 9 - (-3) = 12
change in x-coordinates = 6 - 2 = 4
slope of Line A = 12/4 = 3
For Line B passing through the points (0, 9) and (2, 3):
change in y-coordinates = 3 - 9 = -6
change in x-coordinates = 2 - 0 = 2
slope of Line B = -6/2 = -3
Since the slopes of Line A and Line B are not equal (3 ≠ -3), the two lines are not parallel.
In conclusion, Line A and Line B are not parallel because they have different slopes.