Question

Without graphing,determine whether the following pairs of lines are (a)parallel (b)perpendicular, or (c) neither parallel nor perpendicular

5x-6y=19
6x+5y=-30

Answer 1

Solve for y
y=mx+b
Compare m: it determines parallel, perp

Answer 2

5x-6y=19
-6y = -5x+19
y = (5/6)x-(19/6)
Since this line is expressed in the standard linear form of y=mx+b where m is the slope, so the slope of this line = m1= 5/6

6x+5y=-30
5y = -6x+30
y = (-6/5)x+6
Similarily, since this line is expressed in the standard linear form of y=mx+b where m is the slope, so the slope of this line = m2= -6/5

Since m1*m2 = (5/6)*(-6/5) = -1,then these two lines are perpendicular to each other.