Final answer:
To find the equation of a line perpendicular to y = -1/6x + 9 and goes through the point (3, 8), use the negative reciprocal of the slope of the given line and the coordinates of the point in the equation y = mx + b.
Step-by-step explanation:
To find an equation for a line perpendicular to y = -1/6x + 9 and goes through the point (3, 8), we need to find the slope of the given line. The slope of the given line is -1/6, so the slope of the perpendicular line would be the negative reciprocal, which is 6. Using the slope-intercept form (y = mx + b), we can substitute the slope (6) and the coordinates of the given point (3, 8) to find the equation. Therefore, the equation of the perpendicular line is y = 6x - 10.