Final answer:
The equation of the line that is perpendicular to y = 3x + 1 and passes through (9, 6) is A. y = -1/3x + 9, which is found using the negative reciprocal slope of the given line and applying the point-slope form with the given point.
Step-by-step explanation:
The question involves finding the equation of a line that is perpendicular to another line and passes through a given point. The slope of any line perpendicular to the line y = 3x + 1 would be the negative reciprocal of 3, which is -1/3, because perpendicular lines have slopes that are negative reciprocals of each other. Since the line must pass through the point (9, 6), we can use the point-slope form to determine the equation of the line, which is y - y1 = m(x - x1), substituting in m = -1/3, and the given point (9, 6).
Our equation becomes: y - 6 = -1/3(x - 9). To find the slope-intercept form, we'll simplify the equation by distributing the slope and moving the 6 over to the other side:
y - 6 = -1/3x + 3
y = -1/3x + 3 + 6
y = -1/3x + 9
Therefore, the correct answer is A. y = -1/3x + 9.