Final answer:
The equation of the line perpendicular to y = (1/4)x - 7 passing through the point (3, -4) should have a slope of -4. The correct equation, derived using the point-slope form, is y = -4x - 8. None of the provided options matches this result, suggesting a possible error in the question or options.
Step-by-step explanation:
To find an equation of the line perpendicular to the line y = (1/4)x - 7, we first identify the slope of the given line, which is 1/4. A line that is perpendicular to another in the xy-plane will have a slope that is the negative reciprocal of the original line's slope. Therefore, the slope of the line we are looking for is -4 (negative reciprocal of 1/4).
Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes and m is the slope, we can substitute (3, -4) for (x1, y1) and -4 for m. This gives us:
y - (-4) = -4(x - 3)
Simplifying this equation yields:
y + 4 = -4x + 12
When we move 4 to the other side, we get:
y = -4x + 8
However, this is not among the options provided. Since there was an error with the subtraction of 4 in the last step, the correct equation after the final step should be:
y = -4x - 8
As no option matches this result, there might be an error in the question or the options provided. Hence, none of the provided options is correct based on our calculation.