First, note that parallel lines have equal slopes, and perpendicular lines have negative reciprocal slopes. If I am reading the problem correctly, the equation of line L is:
x + πy = 1
Let's re-write this in slope-intercept form.
πy = 1 - x = -x + 1
y = (-1/π)x + (1/π)
The slope of this line is -1/π. The line parallel to L will have this same slope.
y = mx + b
If the line passes thru point P, then we have:
4 = (-1/π)(-2) + b
4 = (2/π) + b
b = 4 - (2/π)
We have found the y-intercept, so the equation of the line is:
y = (-1/π)x + [4 - (2/π)]
The line perpendicular to L will have a slope of π
4 = π(-2) + b
4 = -2π + b
b = 4 + 2π
y = mx + b
The equation of the line perpendicular to L and passing thru point P is:
y = πx + (4 + 2π)
