# Thread: parallel & perpendicular lines help

1. ## parallel & perpendicular lines help

hey everyone, this is my first post...i hope i can find some help here, as i have searched my math book up and down, only to find no answer.

i am in college algebra, and the section is parallel & perpendicular lines.

the problem i am totally stuck on is this...

Code:

x - y       x + y
-----  =   -----   - 1
3            2

AND

7 = - ( x - y ) + 4y
They want me to rewrite both in slope-intercept form, then find out if they are parallel or perpendicular.

I would really and truly appreciate any and all help with this...i just don't know what to do

thanks so much,

ryan

2. Originally Posted by shipwreck
hey everyone, this is my first post...i hope i can find some help here, as i have searched my math book up and down, only to find no answer.

i am in college algebra, and the section is parallel & perpendicular lines.

the problem i am totally stuck on is this...

Code:

x - y       x + y
-----  =   -----   - 1
3            2

AND

7 = - ( x - y ) + 4y
They want me to rewrite both in slope-intercept form, then find out if they are parallel or perpendicular.

I would really and truly appreciate any and all help with this...i just don't know what to do

thanks so much,

ryan
Hello Ryan,

$\displaystyle \frac{x-y}{3}=\frac{x+y}{2}-1$

First, let's multiply everything by the LCD of 6 to get rid of those pesky denominators.

$\displaystyle 6\left(\frac{x-y}{3}\right)=6\left(\frac{x+y}{2}\right)-6(1)$

$\displaystyle 2x-2y=3x+3y-6$

Simplify to

$\displaystyle -5y=x-6$

$\displaystyle \boxed{y=\frac{-1}{5}x+\frac{6}{5}}$

Now for the other one...

$\displaystyle 7=-(x-y)+4y$

$\displaystyle 7=-x+y+4y$

Simplifying....

$\displaystyle 5y=x+7$

$\displaystyle \boxed{y=\frac{1}{5}x+\frac{7}{5}}$

Compare the slopes of the two boxed equations. What do you think?

3. well i know that if both slopes are identical, than they are considered parallel....but these aren't identical, although i don't know if there is a particular rule or not about them being opposites, but NOT being reciprocal negative opposites...

1/5 x & 1/5x would be parallel, but i am just not 100% certain about 1/5x & -1/5x. i would say they are not parallel...right?

4. anyone able to confirm if i am right or not about these being parallel or not?

5. Originally Posted by shipwreck
anyone able to confirm if i am right or not about these being parallel or not?
You answered your question yourself. If the slopes are not the same then they aren't the parallel