Question

Find the equation of the line through (4,3) perpendicular to the line 3x+y=7

Answer 1

so this is going to be similiar to what we did, but for a perpendicular line, the slope is the opposite reciprocal

Answer 2

it always changes on a perpendicular line?

Answer 3

i'm not sure what you mean

Answer 4

if you have two lines that are parallel, they have the same slope
if you have two lines that are perpendicular, than their slopes are opposite reciprocals

Answer 5

like the slope is the opposite reciprocal?

Answer 6

https://www.purplemath.com/modules/slope2.htm

Answer 7

yeah, for any two lines to be perpendicular, it means their slope are opposite reciprocals

Answer 8

ooo ok got it

Answer 9

you can think of it visually too
if you have two lines that are parallel, it means that they never touch, right? so that means that they're at exactly the same angle, like so:

these two lines will always have the same slope

these lines are perpendicular, meaning they're the exact opposite of each other, and they intersect at a 90degree angle

so if the slope is 5 for one, the slope for the other will be - 1/5

Answer 10

ooo ok yea it makes sense

Answer 11

so using what you learned on the previous problem, can you tell me what the equation is?

Answer 12

ok so i would put 3x+y=7 then it would be y=3x+7 right?

Answer 13

keep in mind that you're not just moving it over, you're actually subtracting it from both sides

Answer 14

o right so it would be y=-3x+7 right?

Answer 15

yup!

Answer 16

so what's the slope of your perpendicular line?

Answer 17

ok so now i do the y-y1=m (x-x2) right?

Answer 18

not quite yet, you don't have your correct slope yet. remember you're looking for the slope of a line that is perpendicular to the line you just gave me

Answer 19

ooo so i multiply -1 to -3 and +7?

Answer 20

na you don't even need to do any manipulation to it, just know that the reciprocal of something is the opposite of it so like
2/3 = 3/2
5/4 = 4/5
1/2 = 2/1
5 = 1/5

and if you're taking the opposite, than it's just going to be negative, if your number is positive, and positive if your number is negative

so the opposite reiprocal of -9 will be 1/9
and the opposite reciprocal of 7/6 will be -6/7

make sense?

so for the line you just gave me, what's its slope and what is its opposite reciprocal?

Answer 21

so it would be 1/3?

Answer 22

yup :o

Answer 23

yay ok so it would be y=1/3+7 right?

Answer 24

well, you just figured out the slope, now as you said before you have to plug in the two points (4,3) into
y-y1 = m (x - x1)
you're almost there!!

Answer 25

ok but when u said 5=1/5 would it be negative too?

Answer 26

i was just giving examples of reciprocals, without adding in the opposite sign yet
the reciprocal of 5 = 1/5, the opposite reciprocal of 5 = -1/5
make sense?

Answer 27

ook but was i right?

Answer 28

which part?

Answer 29

thats 5= 1-/5?

Answer 30

it depends on what you're looking for.. if you're trying to find the opposite reciprocal, then yes

Answer 31

the word opposite means that it changes signs (negative to positive, positive to negative)
the word reciprocal just means that it flips

Answer 32

oo ok thnx ok going on to the other problem plug in the two points

Answer 33

excellent ^.^

Answer 34

ok i hope im right lol i did y-3=1/3(x-4) right?

Answer 35

then i did 3(y-3)=x-4

Answer 36

the first part looks right, but what happened with the y in the second part?

Answer 37

remember, you want to get the y by itself, so you want to keep that 1/3 over on the right

Answer 38

are you familiar with distribution?

Answer 39

yea i am but i thought u leave x were 4 is and 3 on the other side

Answer 40

what you want to do is distribute the 1/3 to the (x-4)

Answer 41

yes

Answer 42

just ignore the left side for now, and try to do the distribution

Answer 43

so u multiply 1/3 with -4?

Answer 44

yup

Answer 45

and the x as well

Answer 46

you're literally just distributing the 1/3 into the (x-4)

Answer 47

u lost me lol

Answer 48

you said you're familiar with distribution right? in this case, you're distributing the 1/3 into the (x-4) so, you're multiplying both terms by 1/3 like so:

(x(1/3) - 4(1/3))

Answer 49

o yea so it would be1/3x but the other 1 i dont know wat it would be

Answer 50

if you're multplying 4 by 1/3 it's the same thing as multiplying 4/1 x 1/3, does that make it easier?

Answer 51

\[\left(\begin{matrix}4 \\ 1\end{matrix}\right) x \left(\begin{matrix}1 \\ 3\end{matrix}\right)\]

Answer 52

ok so it would be 4/3?

Answer 53

yup ^.^

Answer 54

so now, we can look back over at the left side
y-3 = 1/3x+4/3

Answer 55

now, you want to get the y alone, so what should you do?

Answer 56

ok i would move that negative and put it positve and put it on the other side and add 4/3?

Answer 57

yup!!! you got it ^.^

Answer 58

just remember that you can't just add it as it is though, you're dealing with 3/1 + 4/3, so you have to get a common denominator

Answer 59

ok but how would i add 4/3 to 3?

Answer 60

\[\left(\begin{matrix}4 \\ 3\end{matrix}\right) + \left(\begin{matrix}3 \\ ?\end{matrix}\right)\]

Answer 61

oops that ? should be a 1 lol

Answer 62

lol i was gonna say would it be a 1?

Answer 63

basically you want to make it so that the two bottom numbers match, so you want it to be something /3 .. whatever you did to the bottom to get that 3, you have to do to the top as well

Answer 64

\[\left(\begin{matrix}3 \\ 1\end{matrix}\right) = \left(\begin{matrix}9 \\ 3\end{matrix}\right)\], right?

Answer 65

can you see how i got that?

Answer 66

no i dont im srry

Answer 67

so i want to make the bottom match to 4/3 right?
i need to do soething to 3/1 so that it has the same bottom ?/3
i multiplied the bottom by 3, to get ?/3 and whatever i did to the bottom, i have to do to the top as well so 3x3=9 /3

Answer 68

it's kind of hard to explain over text lol

Answer 69

its ok i get it alittle bit

Answer 70

but thank you for trying to explain

Answer 71

when you're adding fractions, the denominators have to be equal.. so if they're not, you have to do something to the bottoms to make them equal,a nd whatever you do to the bottom, you have to do to the top as well

Answer 72

http://www.mathsisfun.com/fractions_addition.html that explains it pretty well