how do i determine whether each pair of lines is parallel, paerpendicular, or niether? prob. example: y=2/9x+3                         y=-2/9x  

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Parallel lines have equal slopes.  Perpendicular lines have slopes that are opposite (e.g., negative) reciprocals of one another (so m1=-1/m2).Since these 2 lines are already in slope-intercept form, you can simply read off the slopes (the coefficient on the x variables).  You have m1=2/9 and m2=-2/9.  These are not equal, nor are they opposite reciprocals.  So, these lines are NEITHER parallel or perpendicular.