Final answer:
The correct coordinate representation of the equation y-12 = 5(x + 3) is option C, (-3, 12), which satisfies the equation when the values are substituted in.
Step-by-step explanation:
The goal is to identify the coordinate represented by the equation y-12 = 5(x + 3). This equation can be rewritten in function form by adding 12 to both sides, resulting in y = 5(x + 3) + 12. Now, to find the specific coordinate that the equation represents, we need to identify a point (x, y) which satisfies the equation. When an equation is written in this form, it typically defines a set of many points that lie on a line and not just a single coordinate pair. However, the way the question is formulated seems to suggest looking for an intercept or special point that is already given among the options.
Picking options from the provided list: A. (12, -3), B. (3,-12), C. (-3, 12), and D. (-12.3), we can substitute these into the original equation to check for validity. Option A is incorrect since substituting x=12 and y=-3 we get -3-12 ≠ 5(12+3). Similarly, Option B is incorrect with 3 substituted for x and -12 for y; -12-12 ≠ 5(3+3). Option D is not even a properly formatted coordinate.
Therefore, by process of elimination and also by direct verification (substituting x=-3 into the equation results in y=12), we can confidently say that the answer is C. (-3, 12).