Select the equations that are parallel and perpendicular to y = −3x − 1 and that pass through the point (3, 1).
A. parallel: y = −3x + 6
perpendicular: y = (1/3)x + 2(2/3)
B. parallel: y = −3x + 10
perpendicular: y = (1/3)x
C. parallel: y = -(1/3)x
perpendicular: y = −3x
D. parallel: y = (1/3)x + 1
perpendicular: y = 3x − 1

- RealityWillSlapYou

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- RealityWillSlapYou

@SmokeysTheName, Right here!

- SmokeysTheName

ohhh man, remember i said i couldn't help? but here @phi might be able to

- RealityWillSlapYou

Oh, oops! Sorry about that.... :)

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## More answers

- SmokeysTheName

thats fine (:

- SmokeysTheName

@hero can you help with this?

- Hero

Pretty easy stuff @SmokeysTheName

- SmokeysTheName

its been forever since ive done this and i can't remember /: so can you help him?

- Hero

Hint:
m1 x m2 = -1

- RealityWillSlapYou

Umm.... I not really sure.. :|

- Hero

m1 = -3
So m2 has to be a number such that when multiplied by m1, their product is -1.

- RealityWillSlapYou

-1?

- RealityWillSlapYou

Then 1 x -1 = -1

- RealityWillSlapYou

Right?

- Hero

m1 = -3
Multiply -3 by something to get -1

- RealityWillSlapYou

I have no clue..... :|

- SmokeysTheName

is that even possible @hero?

- Hero

-3 x 1/3 = -1

- Hero

Yes, it is possible.

- Hero

So that's basically the slope of the second equation.

- SmokeysTheName

oh yeah xD lol i dont like fractions so i didnt think of it. my bad okay ill stay out of this..

- RealityWillSlapYou

Oh, why is math so hard for me to understand?!

- Hero

So now, you have the slope and the point. Use the point slope formula to figure out the value of b.

- RealityWillSlapYou

Y U NO WORK FOR ME MATH?! (ノಠ益ಠ)ノ

- phi

sometimes it helps to watch these videos
http://www.khanacademy.org/math/trigonometry/graphs/parallel_perpendicular/v/equations-of-parallel-and-perpendicular-lines

- SmokeysTheName

phi is right, khan acad vids are great to watch

- RealityWillSlapYou

@phi, in the video he was using two points and my question only has one point so how can I solve it the same way?

- phi

at the very end he does a problem like yours.

- RealityWillSlapYou

Oh, my video sever crashed after the second equation.

- phi

but this video assumes you know about slopes and equations of lines (he has videos on all of that)
for you problem, you should know that when you see
y = mx +b
m is the slope. the number multiplying the x is the slope

- RealityWillSlapYou

I will start it back up again, but it will take 2 min.

- RealityWillSlapYou

I tried to solve it (I think I did it wrong) and is it C?

- phi

for you problem, you should know that when you see
y = mx +b
m is the slope. the number multiplying the x is the slope
so what is the slope of your line
y = −3x − 1
?

- RealityWillSlapYou

-3?

- phi

do you see a number in front of the x ?

- RealityWillSlapYou

So is the answer B?

- phi

yes, -3 is the slope (that is why people came up with this kind of equation, you can read off the slope easily)

- phi

from the video, you learned that parallel lines have what kind of slope ?

- RealityWillSlapYou

The same slope

- phi

look at your 4 choices. which choices have the correct slope of -3 for the parallel line ?

- RealityWillSlapYou

Well it's A or B....... I think it's B

- phi

no need to guess. now for the perpendicular line. Its slope is the negative inverse (or negative reciprocal)
that means "flip" the slope and multiply by -1. For example
if you had slope =2
\[ \frac{2}{1} ->- \frac{1}{2}\]
can you do that for -3 ?

- RealityWillSlapYou

\[\frac{ 3 }{ 1 }?\]

- RealityWillSlapYou

Or\[\frac{ 1 }{ 3 }?\]

- phi

3/1 is 3
start with -3 or -3/1
minus it : - -3/1 is +3/1
now flip it : 1/3
you know you did it right if it is the opposite sign of -3, and it's "upside down"

- RealityWillSlapYou

Okay

- phi

the slope of the perpendicular is 1/3
look at choices A or B. can we rule out either choice because it does not have 1/3 for the slope of the perpendicular line ?

- RealityWillSlapYou

We can rule out A, right?

- phi

for choice A, what is the number in front of the x for the perpendicular line ?

- RealityWillSlapYou

-3

- phi

that is the parallel line

- phi

A. parallel: y = −3x + 6
perpendicular: y = (1/3)x + 2(2/3)

- RealityWillSlapYou

So we rule out B?

- phi

B. parallel: y = −3x + 10
perpendicular: y = (1/3)x
what is the slope for the perpendicular line ?

- RealityWillSlapYou

1/3

- phi

so both A and B pass. we have to use the last bit of info
pass through the point (3, 1)
that says that when x=3 y must = 1
test choice B, perpendicular (because it looks the easiest)
y = (1/3)x
replace x with 3 and do the arithmetic
what do you get ?

- phi

replace x with 3
that means wherever you see an x, put a 3 in its place.

- RealityWillSlapYou

okay give me a min.

- RealityWillSlapYou

y = (1/3)3

- RealityWillSlapYou

??

- phi

yes,
\[y= \frac{1}{3} \cdot 3 \]
you can think of the 3 as 3/1 or
\[y= \frac{1}{3} \cdot \frac{3}{1} \]
when you multiply fractions, multiply top times top and bottom times bottom
you get
\[y= \frac{3}{3} \]
can you simplify this ?

- RealityWillSlapYou

y = 1

- phi

so (3,1) is on this line. this is the choice

- phi

if we put x=3 in choice A, we will not get y=1
btw, we should check the parallel line
can you do that ?
parallel: y = −3x + 10
what do you get if you replace x with 3

- RealityWillSlapYou

-9

- phi

what about the +10 ?

- RealityWillSlapYou

1

- phi

y = −3x + 10
if this does not give you y=1 when x=3 then it is not the line.
But it does give y=1
so choice B.
Does any of this make sense ?

- RealityWillSlapYou

Yeah....

- RealityWillSlapYou

How many more questions can you help me with?

- phi

how many do you have ?

- RealityWillSlapYou

Three, but I'm really bad at math.

- phi

did you post them yet ?

- RealityWillSlapYou

I posted one of them in algebra

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