Final answer:
The lines represented by the equations 3x - 2y = -9 and 2x - 3y = -3 are neither parallel nor perpendicular, as their respective slopes, 3/2 and 2/3, are neither equal nor the negative reciprocal of each other.
Step-by-step explanation:
To determine if the lines represented by the equations 3x - 2y = -9 and 2x - 3y = -3 are parallel or perpendicular, we need to compare their slopes. To do this, we must first put both equations in slope-intercept form, which is y = mx + b, where m is the slope.
For the first equation, 3x - 2y = -9, we solve for y to find the slope:
-2y = -3x - 9
y = (3/2)x + 9/2
Hence, the slope (m1) is 3/2.
For the second equation, 2x - 3y = -3, we solve for y to find the slope:
-3y = -2x - 3
y = (2/3)x + 1
Thus, the slope (m2) is 2/3.
Two lines are perpendicular if the product of their slopes is -1. In this case, 3/2 * 2/3 does not equal -1, so they are not perpendicular. Two lines are parallel if their slopes are equal, which is also not the case here since 3/2 is not equal to 2/3. Therefore, the lines are neither parallel nor perpendicular.