SOLUTION: Hi, I'm new to this so I'm not sure if this is in the right section. Find the distance between each set of parallel lines. y=2x-3 and 2x-y = -4

Algebra ->  Length-and-distance -> SOLUTION: Hi, I'm new to this so I'm not sure if this is in the right section. Find the distance between each set of parallel lines. y=2x-3 and 2x-y = -4      Log On


   

Question 1010351: Hi, I'm new to this so I'm not sure if this is in the right section.
Find the distance between each set of parallel lines.
y=2x-3 and 2x-y = -4
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +y+=+2x+-+3+
(2) +y+=+2x+%2B+4+
--------------
These lines are parallel since their
slopes are both = +2+
---------------------
Find y-intercept of (2)
(2) +y+=+2%2A0+%2B+4+
(2) +y+=+4+
--------------
What is the equation of the line through
( 0,4 ) and is perpendicular to (2) ?
It's slope will be:
+m%5B2%5D+=+-+1%2Fm%5B1%5D+
+m%5B2%5D+=+-1%2F2+
----------------
Use general point-slope formula
+%28+y+-+4+%29+%2F+%28+x+-+0+%29+=+-1%2F2+
+2%2A%28+y+-+4+%29+=+-1%2Ax+
+2y+-+8+=+-x+
+2y+=+-x+%2B+8+
+y+=+-%281%2F2%29%2Ax+%2B+4+
---------------------
Now find the point where this line
intersects (1)
(1) +y+=+2x+-+3+
+2x+-+3+=+-%281%2F2%29%2Ax+%2B+4+
+4x+-+6+=+-x+%2B+4+
+5x+=+10+
+x+=+2+
and
(1) +y+=+2%2A2+-+3+
(1) +y+=+4+-+3+
(1) +y+=+1+
The point is ( 2,1 )
-----------------
Now find the distance between
( 0,4 ) and ( 2,1 )
+d+=+sqrt%28+%28+2+-+0+%29%5E2+%2B+%28+1+-+4+%29%5E2+%29+
+d+=+sqrt%28+4+%2B+9+%29+
+d+=+sqrt%28+13+%29+ answer
---------------------
Here's a plot of the given lines:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2x+-+3%2C+2x+%2B+4+%29+
+sqrt%2813%29+=+3.606+, so this looks pretty close
Hope I got it!