equation of a line

Question

Write equations of the lines through the given point parallel to and perpendicular to the given line.

4x − 2y = 9,    (4, 1)

Answer 1

Parallel lines have the same slope. 4x-2y=9, so y=(4x-9)/2 making the slope 4/2=2.

The line we need looks like y=2x+a where a is what we have to find. Plug in (4,1):

1=8+a so a=-7 and y=2x-7.

Perpendicular lines have the negative inverse of the slope 2, so we have -1/2 as the slope.

y=-x/2+a where we have to find a different a this time. Plug in the given point:

1=-2+a so a=3 and the perpendicular line is y=-x/2+3 which can be written 2y=6-x.