consider the line 6x-3y=-9

Question

Find the equation of the line that is perpendicular to this line and passes through the point
, −3 6
.

Find the equation of the line that is parallel to this line and passes through the point
, −3 6
.

Answer 1

Original line rewritten in a convenient form for our purposes  y = 2x + 3 ;

 

*) y - 6 = (-1/2)(x - (-3)) ⇔ y = -1/2 x - 3/2 + 12/2 ⇔ y = -1/2 x + 9/2  perpendicular to the original.

 

**) y - 6 = (2)(x+3) ⇔ y = 2x + 6 + 6 ⇔ y = 2x + 12  parallel to the original.