Final answer:
The equation of a line parallel to y = -9x - 12 and passing through (4, 1) is found by keeping the same slope of -9 and substituting the point into the point-slope form of the equation. The resulting equation is y = -9x + 37, which is Option 4.
Step-by-step explanation:
To find the equation of a line parallel to y = -9x - 12 and going through the point (4, 1), we must remember that parallel lines have the same slope. The given line has a slope of -9, so our new line will also have this slope. To find the y-intercept, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes.
Plugging in the point (4, 1) and the slope -9, we have y - 1 = -9(x - 4). Simplifying, we get y = -9x + 36 + 1, which simplifies further to y = -9x + 37. Therefore, the correct equation of the line parallel to y = -9x - 12 and passing through the point (4, 1) is y = -9x + 37, which is Option 4.