Answer:
The graphs of y = 3x + 4 and y = 3x + 7 are parallel because their slopes are the same (3).
The graphs of y = 2x - 5 and y = 5x - 5 are neither parallel nor perpendicular because their slopes are not the same (2 and 5).
The graphs of y = 3/5x - 3 and 5y = 3x - 10 are neither parallel nor perpendicular. The first equation is not in slope-intercept form, and the second equation is not in standard form.
The graphs of y = 7x + 2 and x + 7y = 8 are neither parallel nor perpendicular. The first equation is in slope intercept form, but the second equation is not.
The graphs of y = -4x + 1 and 4y = x + 3 are perpendicular because the product of their slopes is -1.
The graphs of y = -1/3x + 2 and y = 3x - 5 are neither parallel nor perpendicular. The slopes are -1/3 and 3, which are not the same, so the lines are not parallel, and their product is not -1, so the lines are not perpendicular.
The graph of y = 4 is a horizontal line and the graph of 4y = 6 is not a function. So, they are neither parallel nor perpendicular.
The graphs of y = 5/6x - 6 and x + 5y = 4 are neither parallel nor perpendicular. The first equation is in slope intercept form, but the second equation is not.
Explanation: