Question

Okay, this is a problem that I've tried over ten times before getting a fresh problem and trying that one too. I've never gotten a correct answer and I can't figure out why it's not right.

Here's the problem,

"Find the distance between each pair of parallel lines."

21.
y=2x+2
y=2x-3"

Could anyone explain to me how to do this problem? I've gotten through it completly, but I think I'm doing /something/ wrong.

Please help. =(


There are a couple ways to solve this problem.
The common method is to find a point on one line, then find it's distance to the other line. Let's find a point on y=2x+2. The point (x1,y1)=(0,2) is the most obvious one to use.

Now write the second equation as
ax+by+c=0 or
-2x+y+3=0
Then use the formula
distance = |a*x1 + b*y1 +c|/sqrt(a^2 + b^2)
where (x1,y1)=(0,2) a=-2, b=1 and c=3
We have distance=|-2*0 + 1*2 + 3|/sqrt(2^2 + 1^2) = 5/sqrt(5) = sqrt(5)
(That's the absolute value of the numerator.)