Final answer:
The equation of the line perpendicular to y = -5/6x - 1 through (5, -2) is y = 6/5x - 8. The equation of the parallel line through the same point is y = -5/6x + 19/6.
Step-by-step explanation:
To find the equation of a line perpendicular to y = -5/6x - 1 that passes through the point (5, -2), we first identify the slope of the given line. The slope of the given line is -5/6, so the slope of a line perpendicular to it would be the negative reciprocal, which is 6/5. Using the point-slope form, the equation is y + 2 = 6/5(x - 5), which simplifies to y = 6/5x - 8.
For the parallel line, since parallel lines have the same slope, the slope remains -5/6. Using the point-slope form again, the equation for the parallel line through (5, -2) is y + 2 = -5/6(x - 5), which simplifies to y = -5/6x + 25/6 - 2 or y = -5/6x + 19/6.