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Question 551994: why are 3x+6y=12 and 6x-3y=9 parallel
Answer by neatmath(302)   (Show Source):
You can put this solution on YOUR website!
In order to solve this question, we need to find the slopes and y-intercepts of the 2 lines.
We can easily do this by solving both equations in terms of y.
 where m is the slope, and b is they y-intercept.
First equation:
Next equation:
Well, we should now realize something important here.
These lines are NOT parallel, they are perpendicular!!!
If they were parallel, they would have the exact same slope (m), and would have different y-intercepts (b).
These lines have slopes (m) that are negative reciprocals.
When 2 lines have slopes that are negative reciprocals,
by definition, they are perpendicular.
If you sketch the lines, you will see that they are perpendicular, and not parallel to each other.
I hope this helps! :)
Email Scott: neatmath@yahoo.com for help with specific problems,
or to inquire about mathematics tutoring via email or other methods.
Paypal is always accepted for single problems or for more intensive tutoring!
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