Question 366561
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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)