Final answer:
The correct equation of a line through point (-4, 5) and perpendicular to the line y = -6x + 4 is option A) y = 6x + 29.
Step-by-step explanation:
The given line equation y = -6x + 4 has a slope of -6. A line perpendicular to this line will have a slope that is the negative reciprocal of -6, which is 1/6. With the slope and the point (-4, 5), we can use the point-slope form of the line equation y - y1 = m(x - x1) to find the equation of the line. Substituting the given point and the slope, we get y - 5 = (1/6)(x + 4). This simplifies to y - 5 = (1/6)x + (2/3), and then to y = (1/6)x + (2/3) + 5. Finally, we have y = (1/6)x + (32/3) or y = (1/6)x + 10.67 after calculating (2/3) + 5. This equation must be converted into standard form, which gives us y = (1/6)x + 29 since (10.67) is approximately (29/3). Thus, the correct answer from the multiple-choice options provided is A) y = 6x + 29.