What's the distance between equations y=2x+3 and y=2x-3

The distance between two parallel lines is the length of the perpendicular segment connecting the two lines.

We find the slope of the perpendicular:


Pick a point on (let's go with ) and find where it intersects

The perpendicular line will be

We have a system of equations:


Solve:

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Plug into :


So our second point is

The distance between the points is:

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So the distance between the two lines is