Hi, 

In both cases put, the lines you are comparing, into the slope intercept form:

y = mx + b  by solving for y and then review their slopes



first ex: lines perpendicular? 

perpendicular lines have slopes that are negative reciprocals of one another

2x – 3y = 5    y = (2/3)x - (5/3)

3x + 2y = 7    y = -(3/2)x + 7/2

Yes, perpendicular -(3/2) is the negative reciprocal of 2/3



second ex: lines parallel? 

parallel lines have slopes that are equal to one another (have same slant)

2x + 3y = 7     y = -(2/3) +(7/3)

4x + 6y = 11    y = -(4/6)x + (11/6)

Yes, parallel  slopes are equal -(4/6) = -(2/3) 

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