Answer: neither
Explanation:
For a graph to be parallel, it must have the same slope.
e.g., y = 2x and y = 2x + 1 are parallel because they both have the slope "2"
For a graph to be perpendicular, its slopes must be the reciprocal of each other, and the sign (positive/negative) is flipped
e.g., y = 2x and y = -1/2x + 1 are parallel because their slopes are reciprocals to each other, and the sign is flipped.
To know whether y = 4x + 3 and 4x + y = 3 are parallel, perpendicular, or neither, we have to identify the slopes and use what was mentioned previously:
Identifying the slope:
y = 4x + 3 slope = 4
4x + y = 3 --> y = -4x + 3 slope = -4
The slopes are different, so they are not parallel
As the slopes are not reciprocals, they are not perpendicular.
The graphs are neither parallel nor perpendicular.