Final answer:
The slopes of both lines are equal to 3, indicating that they are parallel to each other. Lines that are perpendicular have negative reciprocal slopes, which is not the case here.
The completed sentence is: The comparison of the slope is equal so the lines are parallel.
Step-by-step explanation:
To determine whether the lines are perpendicular, parallel, or neither, we need to find the slope of each line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
For the first equation, 6x - 2y = -2, we rearrange it to the slope-intercept form: 2y = 6x + 2 and then y = 3x + 1. Therefore, the slope of the first line is 3.
The second equation is already in slope-intercept form: y = 3x + 12. The slope of this line is also 3.
Since both lines have the same slope, 3, they are parallel to each other. Lines that are perpendicular have slopes that are negative reciprocals of each other. In this case, the slopes are equal, not negative reciprocals.
The completed sentence is: The comparison of the slope is equal so the lines are parallel.