Final answer:
Option C, y = 2x + 6, is the correct choice as it has the same slope but a different y-intercept than the original equation, ensuring it will intersect with the given equation exactly once.
Step-by-step explanation:
To determine which equation, when graphed with 2y – 4x = 12, will form a system with one solution, we need to ensure that the second equation is not parallel to the first equation. For linear equations of the form y = mx + b, where m is the slope and b is the y-intercept, two lines with different slopes will intersect at exactly one point.
The original equation can be rewritten as y = 2x + 6 (after dividing both sides by 2). Looking at the answer choices, we can notice that option A, B, and D all have a slope of 2, which means they are parallel to the given equation and thus not suitable since they would not intersect (or would intersect infinitely if they are the same line, which is not the case here). Option C, however, is not in slope-intercept form, and when we solve for y, we obtain y = 2x + 6, which is not a multiple of our original equation and has a different y-intercept, so it will intersect the given equation exactly once.