Question

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

Answer 1

@SmokeysTheName, Right here!

Answer 2

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

Answer 3

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

Answer 4

thats fine (:

Answer 5

@hero can you help with this?

Answer 6

Pretty easy stuff @SmokeysTheName

Answer 7

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

Answer 8

Hint:

m1 x m2 = -1

Answer 9

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

Answer 10

m1 = -3

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

Answer 11

-1?

Answer 12

Then 1 x -1 = -1

Answer 13

Right?

Answer 14

m1 = -3

Multiply -3 by something to get -1

Answer 15

I have no clue..... :|

Answer 16

is that even possible @hero?

Answer 17

-3 x 1/3 = -1

Answer 18

Yes, it is possible.

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

Y U NO WORK FOR ME MATH?! (ノಠ益ಠ)ノ

Answer 24

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

Answer 25

phi is right, khan acad vids are great to watch

Answer 26

@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?

Answer 27

at the very end he does a problem like yours.

Answer 28

Oh, my video sever crashed after the second equation.

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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
?

Answer 33

-3?

Answer 34

do you see a number in front of the x ?

Answer 35

So is the answer B?

Answer 36

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

Answer 37

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

Answer 38

The same slope

Answer 39

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

Answer 40

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

Answer 41

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 ?

Answer 42

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

Answer 43

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

Answer 44

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"

Answer 45

Okay

Answer 46

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 ?

Answer 47

We can rule out A, right?

Answer 48

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

Answer 49

-3

Answer 50

that is the parallel line

Answer 51

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

Answer 52

So we rule out B?

Answer 53

B. parallel: y = −3x + 10
perpendicular: y = (1/3)x

what is the slope for the perpendicular line ?

Answer 54

1/3

Answer 55

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 ?

Answer 56

replace x with 3

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

Answer 57

okay give me a min.

Answer 58

y = (1/3)3

Answer 59

??

Answer 60

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 ?

Answer 61

y = 1

Answer 62

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

Answer 63

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

Answer 64

-9

Answer 65

what about the +10 ?

Answer 66

1

Answer 67

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 ?

Answer 68

Yeah....

Answer 69

How many more questions can you help me with?

Answer 70

how many do you have ?

Answer 71

Three, but I'm really bad at math.

Answer 72

did you post them yet ?

Answer 73

I posted one of them in algebra