SOLUTION: why are 3x+6y=12 and 6x-3y=9 parallel

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.

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