Final answer:
The lines in a) are parallel, the lines in b) and c) are neither parallel nor perpendicular.
Step-by-step explanation:
To determine if two lines are parallel or perpendicular, we need to compare their slopes. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line.
a) For the equations y = 2x + 1 and y = 2x - 7, both equations have the same slope (m = 2), so these lines are parallel.
b) For the equations y = -3x + 1 and 6y = 3x + 1, we can rewrite the second equation as y = (1/6)x + 1/6. The slopes are different (m = -3 for the first equation and m = 1/6 for the second equation), so these lines are neither parallel nor perpendicular.
c) For the equations 2y = 3x + 1 and 2x + 3y = 7, we can rewrite the second equation as y = (-2/3)x + 7/3. The slopes are different (m = 3/2 for the first equation and m = -2/3 for the second equation), so these lines are neither parallel nor perpendicular.