Question

palace.

Answer 1

Do you know what is the relation between slopes of two parallel lines???

Answer 2

Not quite.. would it be y - 3x = 9?

Answer 3

I am asking about the slope...

Do you know what slope is???

Answer 4

3

Answer 5

See, you are going fast..

Okay..

Can you change the given equation in this form : y = mx + c

What do you get on changing??

Answer 6

You have y + 3x = 9

Can you convert it in the form : y = mx + c ???

Tell me if you can ??

Answer 7

No, I can't could you explain the steps please? :c
So far I could only think of 4 + 3(2) = 9

Answer 8

What was meant was
you have
y + 3x = 9
It will be better if "y" is on one side of the equality and everything else, on the other :)

Answer 9

like? y = 3x + 9

Answer 10

Yes like that but you are still close to it but not right...

Answer 11

Not quite...
See, transposition, the process of transferring terms from one side of the equation to the other, involves CHANGING ITS SIGN.

Answer 12

y + 3x = 9

Here just subtract 3x from both the sides..

And tell me what did you get??

Answer 13

y = 6

Answer 14

I think you may have committed an error of adding dissimilar terms...
y + 3x = 9
Transposing 3x, or, in other words, adding (-3x) on both sides of the equality
you get ....?

Answer 15

You cannot apply operations like add subtract etc on unlike terms..

3x and 9 are unlike terms, you cannot subtract them..

Answer 16

Let us come to point now:

you can subtract this : 9x - 3x = 6x

But you cannot subtract : 9 - 3x

Now tell me on subtracting 3x from both the sides what did you get ??

Answer 17

6x

Answer 18

Oh wait no.

Answer 19

Just kidding.

Answer 20

Wouldn't be 9x = 3x?

Answer 21

See:

y + 3x = 9

Just show what is the next step you will do when I say you that subtract 3x from both the sides..

Answer 22

Don't actually subtract them but just show...

Answer 23

y + 3x-3x = 9-3x

Answer 24

Yep...

Now slowly solve left hand side only...

Answer 25

Would it be y + 0x or...?

Answer 26

Yes... but do you really need to add 0x?
What is 0x?

Answer 27

y + 0x?/

What is 0x ???

Answer 28

What do you get when you multiply 0 with x ??

Answer 29

It's just 0

Answer 30

That's right, now what do you get when you add y to 0?

Answer 31

Then finally what did you get ??

Answer 32

y

Answer 33

Yep...

So, now write left hand side and right hand side both..

Answer 34

y + 0 = 6x?

Answer 35

Why are you writing y + 0 ??

Any special reason for this??

y + 0= y you just said..

And now what did you get : 9 - 3x = ??

Answer 36

Once again, you seem to have added unlike terms...
Here's a recap
y + 3x = 9
And then you subtracted 3x from both sides of the equation
y + 3x - 3x = 9 - 3x
And then you simplified
y + 0x = 9 - 3x
And then we confirmed that
y + 0x = y
So now, your equation shoud look like...?

Answer 37

I just said, 9 and 3x are not like terms, you cannot operate these..

See, like terms are : 9 and 3 or 3x and 9x or \(9x^2\) and \(3x^2\)..

Unlike terms are : 9 and 3x, 9x and 3 etc..

You cannot operate unlike terms, you cannot add or subtract them..

Answer 38

okay so how is this going to work? I am confused..

Answer 39

When in doubt, don't simplify just yet...
You ended up with
y + 0x = 9 - 3x
And then worked out that
y + 0x = y

Work from there...

Answer 40

isn't that already true though? if I work from there would I subtract 0?

Answer 41

Well, since
y + 0x = y
you could just replace the
y + 0x in
y + 0x = 9 - 3x
with y...

Could you do that?

Answer 42

See you can write y + 0x = y + 0 = y

Instead of writing y + 0 you can simply write it as y..

So:

You got : y = 9 - 3x

Getting ??

Answer 43

Yes, this is going to help find the y-intercept?

Answer 44

Yes, it will..

Keep patience..

Now can you tell the slope(m) by comparing the both:

y = mx + c

y = -3x + 9

What is value of m here ??

Answer 45

-3

Answer 46

Yep, so slope is -3 here..

Now, question says that, line \(l\) is parallel to line y + 3x = 9

So, there is a property that says, Slope of two parallel lines are equal..

So, if y + 3x = 9 has slope of 3, then what is the slope of line \(l\)?? can you tell ??

Answer 47

Wouldn't it still be 3 since it's equal?

Answer 48

Sorry slope is -3..

Answer 49

See, there are two lines given in your question..

Answer 50

First line is \(l\) that is parallel to other line having equation of y + 3x = 9.

And slope of other line is -3, so what will be the slope of line \(l\) ??

Answer 51

It would be 3 this time right

Answer 52

How?
can you explain what logic you are applying here ??

Answer 53

Well you told me that the l that is parallel to y + 3x = 9 has the slope of 3.

Answer 54

Sorry, that was my mistake.. Dear, you have earlier found the slope as -3..

Can't you??

I forgot to write minus sign in front of 3..

Now, I am finally saying that if line y + 3x = 9 has slope of -3, then what is the slope of line\(l\) that is parallel to it..

And always remember: Two parallel lines have equal slope..

Can you tell now??

Answer 55

-3

Answer 56

Yep, so the line \(l\) has slope of -3.

Now you know slope -3 and you have one point given through which the line l passes, can you find its equation ??

Answer 57

4 = -3(2) + b

Answer 58

Carry on..

Answer 59

4 = -6 + b

Answer 60

Yep, go ahead..

Answer 61

Find b here, that is the intercept here..

Answer 62

4 = -6 + 10

Answer 63

See : you are doing it right but your way you are writing it is wrong..

Look it here :

You have :

4 = -3(2) + b

Calculate b from here:

4 = -6 + b

Add 6 both the sides:

\(4 + 6 = \cancel{-6} + b + \cancel{6}\)

you will get :

10 = b

So, value fo b is 10..

Answer 64

Oh alright, so y-intercept = 10?

Answer 65

Getting ??

Answer 66

Yes, I see what you did there.

Answer 67

Well Done..

Answer 68

You gave a great explanation to changepast @terenzreignz

A medal to you for your patience in helping him too..

Answer 69

Danke schön :D

Answer 70

What is it and in which language it is in ??

Answer 71

lol it's in German
It means Thanks
And I really am thankful; That was fun

Answer 72

That two words mean thanks or only one of out of them ??

Answer 73

You really want to discuss that here?
lol
It's probably a language thing, like in Spanish, "Gracias" is taken to mean "thanks" even though it literally means "graces" :D
As for "Danke schön", I believe it literally means "I thank beautifully" :D

Answer 74

Okay...
Dhanyawad... (In Hindi)..