How do you determine if the lines #-12x+9y=15# and #-4x+3y=5# are paralle , perpendicular or neither?

1 Answer
Mar 27, 2015

I would look at the slope of the lines represented by these equations (it representes the inclination of the lines):

first write them isolating #y#;
1) #y=12/9x+15/9=4/3x+5/3#
and
2) #y=4/3x+5/3#

The slope is the coeficient of #x#;

You can have:
1) same slope=parallel lines;
2)slope1=-1/slope2 =perpendicular lines;
3) slope1#!=#slope2 crossing lines.

In this case they are parallel (and coincident).