Final answer:
After finding the slopes of both lines, Line 1 with a slope of -3 and Line 2 with a slope of 3, we determine that the lines are neither parallel nor perpendicular since their slopes aren't equal nor negative reciprocals of each other.
Step-by-step explanation:
To determine if lines are parallel, perpendicular, or neither, we need to consider their slopes. Two lines are parallel if they have the same slope, perpendicular if the product of their slopes is -1, or neither if they do not meet the criteria for being parallel or perpendicular.
Line 1 is given in slope-intercept form as y = -3x + 9, indicating a slope of -3. To find the slope of Line 2, which is given in standard form as 9x - 3y = 4, we must first rearrange it into slope-intercept form (y = mx + b). After rearranging we get y = 3x - 4/3, which gives us a slope of 3.
Since the slopes are negative reciprocals of each other (the product of -3 and 3 is -9, not -1), the lines are neither parallel nor perpendicular.