Original line: y = -5/6x - 1
A line that is parallel to the original will have the same slope. To find the new y-intercept, we'll take the original line, plug in the given point, and solve for b.
y = -5/6x + b
-2 = -5/6(5) + b
-2 = -25/6 + b
b = 13/6
Parallel Line: y = -5/6x + 13/6
A line that is perpendicular to the original will have the opposite reciprocal slope. To find the new y-intercept, we'll take our perpendicular slope, plug in the given point, and solve for b.
y = 6/5x + b
-2 = 6/5(5) + b
-2 = 6 + b
b = -8
Perpendicular Line: y = 6/5x - 8
Hope this helps!! :)