Final answer:
The equation of the line perpendicular to y = 12x + 12 and passing through the point (2,4) is y = -1/12x + 11/6.
Step-by-step explanation:
To find the equation of the line that is perpendicular to y = 12x + 12 and passes through the point (2,4), we need to determine the slope of the line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. The given line has a slope of 12, so the perpendicular line will have a slope of -1/12. Now we can use the point-slope formula to determine the equation of the line.
The point-slope formula is y - y1 = m(x - x1), where (x1,y1) is the given point and m is the slope. Substituting (2,4) for (x1,y1) and -1/12 for m, we get y - 4 = -1/12(x - 2). Simplifying this equation, we have y = -1/12x + 9/6 + 4, which simplifies further to y = -1/12x + 11/6.