Question

Write an equation for a line perpendicular to y = -3 x + 3 and passing through the point (-6,-4) how do I do this?

Answer 1

to make a line perpendicular, you take the current slope and times it by -1 and take the recipricle of it.
so if my slope was 3, then I do -1*3 = -3, then the recipricle is -1/3 (a fraction) make sense so far?

Answer 2

Yes because m1*m2 = -1 correct?

Answer 3

great, so your slope is going to be 1/3, the next part is...

Answer 4

you mean -1/3?

Answer 5

to take the standard slope intercept equation form, and plug in our new values:

y =mx+b <-slope intercept form
we have m, and are given x and y as the 'point the new line must pass through'
so substitue in the values that you can right now and show me what you get

Answer 6

therefore b=6?

Answer 7

-6

Answer 8

and to answer yout question, it is 1/3.

see, we have -3 as m, then we times it by -1, so
(-1)*-3 = 3 then
we take the recipricle, so 3 becomes a fraction
1/3

Answer 9

it would be -6 if our slope was -1/3, but our slope needs to be 1/3 inorder to have the new line be perpendicular
ya? make sense? ask all you want, i'm here to help you

Answer 10

Okay so if m1 is -3 then m2 is unknown correct?

Answer 11

in order to find m2 we multiply -1*-3?

Answer 12

or do we put it into a fraction?

Answer 13

m2 means the slope of the new line we are looking for, which is perpendicular?

Answer 14

correct

Answer 15

"in order to find m2 we multiply -1*-3?" this idea is right, yes

Answer 16

okay which would in turn = 3 not 1/3

Answer 17

m2 = m1 * (-1) <- part 1 of finding the slope of a line perpendicular

part 2 of finding the slope of a line perpendicular is taking the 'opposite form' of m2 which we got from the part just above.

so if part 1 had m2 = 1/4, then part 2 is to take the 'opposite form' or flip m2, like this:
1/4 becomes 4

Answer 18

here are some examples:

m1 = 5
m2 = (-1)*5 = -5 Part 1
then we flip it in part 2 so now
m2 = -1/5

another example
m1 = -1/8 so,
m2 = (m1) * (-1) = (-1/8) * (-1) = 1/8 then flip it
1/8 becomes 8 so
m2 = 8

Answer 19

Oh okay, I see what your saying, that makes sense now. So in turn since we got -3 it would come out too -3/1 which would give us 1/3

Answer 20

bingo!
that is exactly what you do every time you want find the slope of a line perpendicular to a given line

Answer 21

so my equation would look like y=1/3x +2 ?

Answer 22

yes,
all except I got -2 not 2, let me double check...

Answer 23

yes
it is -2 I messed up on my math

Answer 24

so, when solving for b, your equation should look like this:
-4 = (1/3) * (-6) + b

Answer 25

oh ok ok ya you got it!

Answer 26

so just to re-cap, when ever you want to find the slope of a perpendicular line, you times it by -1 and flip it.

Answer 27

okay
and for a parallel line its m1=m2?

Answer 28

yes, you got it!

Answer 29

I wrote m1*m2=-1 for a perpendicular line.

Answer 30

That's what the professor wrote down.

Answer 31

ya, he is right

Answer 32

then you just have to flip m2

Answer 33

Could you show an example so if we have m1 = -3 and m2= 1/3 what would you do?

Answer 34

oh never-mind just answered my own question!

Answer 35

Well you have been great help thank you very much!!!

Answer 36

you are welcome!
good job on asking questions

Answer 37

Yeah thanks, I love this site such a big help for me sometimes. Well have a good night appreciate the help.