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

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) $y = \frac{12}{9} x + \frac{15}{9} = \frac{4}{3} x + \frac{5}{3}$
and
2) $y = \frac{4}{3} x + \frac{5}{3}$

The slope is the coeficient of $x$;

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

In this case they are parallel (and coincident).