Question

Find the equation of the line that passes through (4,3) and is parallel to the line 3x-y=7 plz help

Answer 1

so first you want to figure out the slope. if two lines are parallel, it means they have the same slope. can you tell me what the slope is of 3x-y=7?

Answer 2

im looking at the textbook and it doest show me how to find the slope

Answer 3

once you have the slope, you want to plug the two points (4,3) into the point-slope form:
Y-Y1 = m (x - x1) where m is the slope and x1 and y1 represent the given point

Answer 4

do you know how to put 3x-y=7 into slope intercept form, where y=mx+b
where m = slope, and b = the y intercept?

Answer 5

no i dont can u plz show me?

Answer 6

of course ^.^ so basically you want to make 3x-y=7 look like y=mx+b

Answer 7

so what do you think would be the first step, to try to get that y alone?

Answer 8

ok so im guessing b is the y-intercept right?

Answer 9

yup, but you want to get that y alone to figure out the slope

Answer 10

i have no clue im srry

Answer 11

no worries
so you have this equation
3x-y=7, and you want to get the y alone - basically move everything from one side of the equation, to the other, until y is by itself..
first thing you want to do is move that 3x over, and you can do that by subtracting it from both sides

if you do that, you're going to cancel it out on the left side, and "add it in" on the right side.. does that make sense?

so you're going to have -y=-3x+7

Answer 12

now that looks a lot more like y=mx+b, right? but we don't want the y to be negative.. what do you think we should do to make it positive?

Answer 13

ok u have to take out the 3x?

Answer 14

yeah, that's the first step, and then you want to make the y positive

Answer 15

make the y positive by i dont know how

Answer 16

you can do that by multiplying the y by -1, and whatever you do to one side of the equation, you have to do to the other.. so this is what it looks like:

(-1)y=(-3x+7)(-1) or (-1)(y)=(-1)(-3x)+(-1)(7))
does that make sense?

Answer 17

can you tell what the final equation is?

Answer 18

oops (-1)(-y) ^.^

Answer 19

ok so it would be y=4x-7?

Answer 20

why 4x?

Answer 21

omg i mean positive 3x lol

Answer 22

perfect :D so now you have the equation y=3x-7 and you know that the form is y=mx+b
where m = slope and b= y intercept..
so.. whats the slope, and y intercept?

Answer 23

the slope would be 3x and -7 would be the y intercept right?

Answer 24

almost! since its mx+b, the slope is JUST the number before the x, which is 3 but you got the y intercept correct ^.^

Answer 25

so now that you know the slope, you want ot take your point, (4,3) and plug it into the slope-intercept form which s
Y-y1=m(x-x1) where your point is (x1,y1) and m = your slope

Answer 26

go ahead and try it, and see what you come up with

Answer 27

ok wait the m=3x?

Answer 28

m is just 3

Answer 29

x is just x

Answer 30

oo ok wait let me c wat i get

Answer 31

ok so i got 3x+3y=-3 am i right?

Answer 32

not quite, remember you're only plugging your 4 and 3 where it says x1 and y1

Answer 33

so in this case, x1=4, and y1=3
y-y1=m(x-x1)

Answer 34

wana try one more time?

Answer 35

yea sure thnx hold on

Answer 36

so would it be x+3y=14?

Answer 37

you want to get the y alone, here i'll show you
y-y1=m(x-x1)
y-3=3(x-4), i distributed the 3
y-3 = 3x -12, and here, you want to get the y alone so you move the 3 over by adding 3 to both sides
y=3x-9

Answer 38

that is the equation of the line that has a slope that is parallel to the first equation, and that passes through the points (4,3) ^.^
does that process make sense? do you want to recap?

Answer 39

ooo ok it makes sense now thank you sooooo much!!!!

Answer 40

but i have a question

Answer 41

so first, you want to find the slope, and since that first line is parallel to your desired line, you know that the slope will be equivalent... you want to get it into the y=mx+b form though to know what m is

then, using point slope form, the two points you were given, and the slope you found, you find the new equation of the line
y-y1=m(x-x1)

Answer 42

how dpo u find the slope cuz i look at the textbook and it wont give me a example can u plz expalin? so i could lean how to?

Answer 43

sure, there are a few ways to do it.. so if you know that y=mx+b, and m = slope
any time you see an equation of that form, you'll know what the slope is.. so like
y=5x+7, slope = 5
y=2x+3, slope = 2

Answer 44

two parallel lines will have the same slope, so if you know the slope of one, you'll know the slope of the other, and you can just identify it, again, by what number is before the x

Answer 45

however, if you're not given an equation, but instead are given two points, there's a formula to find the slope...
\[(y2-y1)/(x2-x1)\]

where your two points are:
(x1,y1)
(x2, y2)

Answer 46

ok cuz in my textbook there an example x-3y=6 and (-1,3) and the slope is 1/3 how is that possible?

Answer 47

so for example, you're given the two points

(1, 2) and (3,4)
(x1, y1) (x1, y2)

and you just plug them into the equation

4-2 / 3 -1 to get 2/2 or = 1

Answer 48

so in this case, you want to again get the y by itself.. do you remember how to do that?

Answer 49

u move everything to the other side?

Answer 50

yup :o so walk me through the steps, what would i do first?

Answer 51

this one is more tricky but i guess u would y alone and put on the other side 3?

Answer 52

wait, run that by me one more time lol

Answer 53

huh? lol

Answer 54

i'm not sure what you just said haha, what would be my first step, if i was trying to solve this?

Answer 55

u would move 3 on the other side to get y alone?

Answer 56

yeah, but how would you move it?

Answer 57

and that's actually not the first thing you want to do - i'll explain why in a second

Answer 58

yea i have no clue cuz it doesnt make sence how the slope would be 1/3 and ok lol

Answer 59

it actually is! i'll explain

so you have x-3y=6, you said that you want to move the 3 over, the only way to move the 3 over would be to divide by 3, right? because to move things over, you want to do the opposite to what's being done to them, and in this case 3 is being multiplied by y, however, you can't just divide the -3y by 3, because the x is there too, you have to divide that by 3 as well.. so my suggestion would be to move the x over first.. how would you do that?

Answer 60

ok so if i divide -3 with 6 it would be -2 right?

Answer 61

yeah, it will, but you still have that x on the left side, and if you divide by -3, you have to divide that entire side by -3, not just the y.. so you can do it that way if you want, this is what you'll get

x/-3 + y = -2

Answer 62

so now what do you do to get it into y = mx+b?

Answer 63

so it would be y=1/3x -2?

Answer 64

yup!!! ^.^

Answer 65

you understand why though right, you're not just looking at the book? :(

Answer 66

well how do u get the 1 over the 3 wouldnt it be just 3?

Answer 67

thats why i said it'd be easier if you moved the x over first
x-3y=6, subtract the x from both sides you get
-3y = -x +6
then you divide by -3 to get the y alone, and whatever you do to one side you have to do to the other
y = (-x + 6)/-3 or y = -x/-3 + 6/-3

Answer 68

y= x/3 -2

(1/3)(x) is equivalent to x/3 because you're just multiplying the x in and out of that 1

Answer 69

make sense?

Answer 70

omg yes it does lol thank you but can u help me with my other problem?

Answer 71

go ahead and close this one and ask again cuz this is starting to get super laggy

Answer 72

ok thank you

Answer 73

for sure ^.^

Answer 74

wait let me just copy everything plz

Answer 75

just the first 1 problem

Answer 76

take your time haha no one's answering my questions so i'll be here for a while

Answer 77

ok thank you

Answer 78

you can actually close this one, and start a new one, and still look at this one while i answer the new one haha

Answer 79

ok i have a question about the first problem

Answer 80

o wait nvm got it lol

Answer 81

ok im done ima close this 1 and start a new one