SOLUTION: • How can you determine if two lines like: 2x – 3y = 5 & 3x + 2y = 7 are perpendicular? • How about also showing the two lines: 2x + 3y = 7 & 4x + 6y = 11 are parallel?

Algebra ->  Linear-equations -> SOLUTION: • How can you determine if two lines like: 2x – 3y = 5 & 3x + 2y = 7 are perpendicular? • How about also showing the two lines: 2x + 3y = 7 & 4x + 6y = 11 are parallel?       Log On


   

Question 366561:
• How can you determine if two lines like: 2x – 3y = 5 & 3x + 2y = 7 are perpendicular?
• How about also showing the two lines: 2x + 3y = 7 & 4x + 6y = 11 are parallel?

Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Convert each line to slope-intercept form,y=mx%2Bb.
Parallel lines have identical slopes, m%5B1%5D=m%5B2%5D.
Perpendicular lines have slopes that are negative reciprocals, m%5B1%5D%2Am%5B2%5D=-1.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


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)