Question

Indicate the equation of the given line in standard form.

The line that contains the point Q( 1, -2) and is parallel to the line whose equation is

y - 4 = 2/3 (x - 3)

Answer 1

parallel lines have the same slope

\(y - y_1 = m(x- x_1)\)

where m is the slope

what is the slope of the equation they gave you?

Answer 2

2/3

Answer 3

\(y - y_1 = \frac{2}{3}(x- x_1)\)

now plug in the point (1, -2)

Answer 4

-2 - y1 = 2/3(1 - x1)

Answer 5

I also have to put it in in the form of _ _ - _ _ _ _

Answer 6

replace y1 with -2 not y with -2
replace x1 with 1 not x with 1 :)

you need it in y = mx + b form?

Answer 7

No, standard form.
so it would be y+2 = 2/3(x-1)?
And then I'd put that in standard form?

Answer 8

Also I cannot put fractions or decimals.

Answer 9

yes, so let's multiply both sides by 3 to get rid of the fraction

Answer 10

^ good idea :-D

Answer 11

so y+6 = 2(x-3)
And then distributive properties
y+6 = 2x - 6
Correct?

Answer 12

Nope, y + 6 should be 3y + 6, right?

Answer 13

when you multiply 3 on one side, you have to do it on the other side too

Answer 14

Right, I was thinking alike properties, so
3y + 6 = 6x - 6?

Answer 15

I will be right back. I'm leaving you in good hands. :)

Answer 16

Alrighty.

Answer 17

Yes, now put it into standard form: ax + by = c where a, b, and c are integers.

Answer 18

What should I do with the +6 and the -6?

Answer 19

Can both be C?

Answer 20

Yes. Combine them on one side.

Answer 21

So 0?

Answer 22

Nope. Subtract 6 from both sides.

Answer 23

Not sure why I thought they'd cancel each other out. So I would get -12?

Answer 24

Yes.

Answer 25

So then I'd have to subtract 3y so I could get 6x - 3y = -12?

Answer 26

3y + 6 = 6x - 6?

We have to look at the big picture. :)

If we subtract 6 on both sides

3y + 6 - 6 = 6x - 6 - 6

3y = 6x - 12

If you bring 3y on to the other side, it's not getting any closer to Standard Form. You could bring 6x to the other side and then multiply both sides by -1. Or you can bring 3y to the other side and then take -12 to the other side by adding 12 on both sides.

Answer 27

3y + 6 = 6x - 6

3y + 6 - 6 = 6x - 6 - 6

3y + 0 = 6x -12

3y = 6x -12

Answer 28

Standard form $$\Huge ax + by = c$$ where a, b and c are integers.

Answer 29

Ah right, I'm doing this all n my head which is never good. But I don't have anything to write on besides notepad.

So, subtract 6x to get -6x + 3y = -12
But since x is supposed to be a non-negatie it would be 6x - 3y = 12
Correct?

Answer 30

That's why I suggested multiplying both sides by -1

Think of it like this

a + b is the same as b + a

(-6x) + (3y) is the same as (3y) - (6x) which would be 3y - 6x

But we want it to be Ax + By

So multiply both sides by -1

-6x + 3y = -12

Also, you can always type out your work on here and post it (:

Answer 31

It doesn't fit, so should I divide by 2?

Answer 32

Mhmm, 3 isn't divisible by 2

Answer 33

Oh! Then 3.

Answer 34

Yes. Divide both sides by 3.

Answer 35

Alright, so now I have 2x - y = 6
The reason I have it as minus is because in the squares there's a forced subtraction symbol.

Answer 36

Alright. I have 3 more, should I just open another discussion?

Answer 37

You went from
-6x + 3y = -12

to
6x - 3y = -12

We'll need to backtrack a bit :)

Answer 38

Think of it like this
a + b is the same as b + a

(-6x) + (3y) is the same as (3y) - (6x) which would be 3y - 6x

But we want it to be Ax + By

So multiply both sides by -1
-1(-6x + 3y) = -1(-12 )

Answer 39

Yes, I had 6x - 3y = 12 not -12

Answer 40

Uh-oh

We made a mistake in the beginning of the question. Earlier above, you changed it from (x-1) to (x-3)

So starting from scratch:

y+2 = 2/3(x-1)
3y + 6 = 2(x - 1)
3y + 6 = 2x - 2
3y + 8 = 2x

And you can complete the last step :P

Answer 41

What about when we multiplied everything by 3 to make 2/3 into 2?

Answer 42

That only affects the 2/3

Answer 43

Not the ( x - 1 )

Answer 44

y+2 = 2/3(x-1)

Multiply both sides by 3