Final answer:
The equation representing the slope-intercept form of a line passing through (12, 9) and perpendicular to y = -34x + 1 is y = (1/34)x - 11/17.
Step-by-step explanation:
The equation that represents the slope-intercept form of a line passing through the point (12, 9) and perpendicular to the graph of y = -34x + 1 can be found by considering that the slope of a perpendicular line is the negative reciprocal of the original slope.
Given that the original line has a slope of -34, the perpendicular line will have a slope of 1/34. Using the point-slope form of a line, we have y - 9 = (1/34)(x - 12). By rearranging this equation, we can obtain the slope-intercept form: y = (1/34)x - 11/17.
Therefore, the correct answer is option A: y = (1/34)x - 11/17.