Final answer:
Both lines represented by the equations y=12x+4 and y=12x+14 have a slope of 12 but different y-intercepts, confirming that they are parallel.
Step-by-step explanation:
To determine whether the lines represented by the equations y=12x+4 and y=12x+14 are parallel, we must compare their slopes. In linear equations of the form y = mx + b, where m is the slope and b is the y-intercept, parallel lines must have identical slopes but different y-intercepts.
In this case, both lines have a slope of 12. The only difference between them is the y-intercept: one is 4 and the other is 14. This means that the lines never intersect and are indeed parallel. Thus, the lines represented by the equations y=12x+4 and y=12x+14 are parallel.