Find the distance between each pair of parallel lines: y=3x-1 and y=3x-11. Can somebody explain the steps to me and also give me the answer? God bless anyone who helps

Question

anonymous · Answer

You can find the perpendicular line function to these parallel line:

$$y = -\frac{1}{3}x$$

Set this equation equal to both of the prior functions and find the two points where they cross.  Then find the coordinates of the two points and use the distance function.

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anonymous · Answer

so would it be -1/3x = 3x-1 and -1/3x = 3x - 11? If I'm not doing this right can you explain in more detail? Please, this is a lesson that my teacher did not go over.

anonymous · Answer

Yes you will then find two values for x.  set them as x1 and x2, then find y1 and y2. Make sense?  You are on the right path.

anonymous · Answer

Oh that makes so much more sense! Thank you so much :)

anonymous · Answer

Wait but then that makes both of the x's a 1...

anonymous · Answer

Can you work out the problem for me? There are more problems like this and I just want to get an idea of how this is set up and how its done so then i could apply this to the other problems