Final answer:
The lines represented by the given equations are perpendicular to each other.
Step-by-step explanation:
The given equations are:
Equation 1: 6x - 2y = -2
Equation 2: y = 3x + 12
We can determine if the lines represented by these equations are perpendicular, parallel, or neither by comparing their slopes.
The slope of a line can be determined by rearranging the equation into slope-intercept form (y = mx + b), where 'm' is the slope.
Comparing equation 1 and 2, we can see that the slope of equation 1 is -3/1 and the slope of equation 2 is 3/1.
Since the slopes of the lines are negative reciprocals of each other (-3/1 and 1/3), the lines are perpendicular to each other.