Final answer:
To find the equation of a line perpendicular to y = (1/3)x + 4 and passing through (1,2), we calculate the negative reciprocal of the given slope (1/3), which is -3, and then use the point-slope form. The equation is y = -3x + 5, which doesn't match any of the provided options.
Step-by-step explanation:
To write the equation for a line that is perpendicular to y = (1/3)x + 4 and passes through the point (1,2), we need to determine the perpendicular slope and use the point-slope form of a line.
The given line has a slope of 1/3; therefore, the slope of the line perpendicular to it will be the negative reciprocal, which is -3. Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through, and m is the slope, we substitute (1, 2) for (x1, y1) and -3 for m.
So, the equation becomes:
y - 2 = -3(x - 1)
Expanding this, we get:
y - 2 = -3x + 3
Adding 2 to both sides gives us the final equation:
y = -3x + 5
However, none of the options provided matches this result. There might be an error in the question or the provided options.