Question

Find equations for the lines through the point (a,

Answer 1

The line y = mx + c has a slope of m.

Parallel line:
A parallel line will also have a slope of m, and should be of the form
y = mx + k
Because the line passes through the point (a,b), therefore
ma + k = b
k = b - ma
The equation of a parallel line is
y = mx + b - ma
   = m(x-a) + b

Perpendicular line:
A perpendicular line will have a slope of -1/m, because the product of slopes should be -1.
The equation for a perpendicular line is of the form
y = -(1/m)x + k
Because the line passes through (a,b), therefore
-(1/m)a + k = b
k = b + a/m
The equation for a perpendicular line is
y = -(x/m) + b + a/m 
   = -(1/m)(x-a) + b

Answer:
Parallel line: $y=m(x-a)+b$
Perpendicular line: $y=- \frac{1}{m}(x-a)+b$