how do you find the distance between these two parallel lines, on a graph using a point and a perpendicular line? y=2x+10 and y=2x-6

Question

jamesj · Answer

Yes, and that perpendicular line has slope -1/2.  Pick an easy first point, say P = (0,10), which sits on the first line.

Then the equation of the perpendicular line is

y - 10 = (-1/2)x

y = -x/2 + 10

Now find where this line intersects the second original line, at a new point Q say.  Then calculate the distance PQ.

anonymous · Answer

my teacher said something about setting it the new equation equal to one of the other equations. which equation would i set it equal to and why?

jamesj · Answer

You now set it equal to the second equation because we're looking the point on the second line that is also on the perpendicular line.

It will be much clearer to you if you sketch a diagram.  I strongly recommend you do that so you can see what's going on.

Show the two original line.  Mark P.  Then draw in the new line whose equation I wrote above.  You'll see roughly where Q is on the second line.  Now find it algebraically.