Question

Describe how you can tell whether two lines are parallel, perpendicular, or neither without graphing them.

Answer 1

Look at the slopes (m)
If the slopes are equal, they are parallel.
If the slopes are "negative reciprocals," they are perpendicular.

Negative reciprocal:
\[m \rightarrow -\frac{ 1 }{ m }\]

Answer 2

or another way to say what DDCamp said is,

let m_1 be the slope of the first line, and let m_2 be the slope of the second line.
if \[m_1*m_2=-1\], then they are parallel

Answer 3

@DemolisionWolf That would be perpendicular, just a typo I'm assuming.

Answer 4

haha my bad

Answer 5

So how do you know if it's neither?

Answer 6

", then they are perpendicular"

Answer 7

if m_1 = m_2, they are parallel
if m_1*m_2=-1, they are perpendicular
if neither is the case, then they are just two lines that will intersect somewhere.

Answer 8

or the same exact line
like
12=2x+4
6=x+2

Answer 9

Well thank you @DemolisionWolf @DDCamp @zpupster c:

Answer 10

parallel no solutions
perpendicular 1 solution
same line infinite no of solutions

Answer 11

zpupster is right too,
tons of good info on this post for you ^_^

Answer 12

Oh goodness, thank you, this has helped a lot cx

Answer 13

Though with @zpupster's method, you have to be careful. Lines that aren't perpendicular also have 1 solution to the system (if they're not parallel or the same).

Answer 14

Oh well, I look out for that c:

Answer 15

I'll*

Answer 16

true