Final answer:
The lines given by the equations y = -4x - 2 and 12x + 3y = 27 are parallel.
Step-by-step explanation:
The given equations are: y = -4x - 2 and 12x + 3y = 27.
To determine if the lines are parallel, perpendicular, or neither, we need to compare their slopes.
The slope of the first equation is -4 and the slope of the second equation can be found by rearranging it into slope-intercept form: 3y = -12x + 27, which becomes y = -4x + 9.
Since the slopes of both equations are equal (-4), the lines are parallel.