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- anonymous

find the equations of the following line:
(v) parallel to 2x+3y=4 and passing through (2,2)
I got the answer y=2x-2 but the answer the book gives is 2x + 3y=10 . Please can you help me by telling me the proper method to find out the answer! Also I realize that you had to rearrange the equation, but what dictates when you have to and when you don't?

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- anonymous

- jamiebookeater

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- Loser66

Show your work, please.

- Loser66

Want to take a trick?

- anonymous

Ok, so I tried a couple ways. First way:
I drew a rough graph to find where the line goes through the y axis using the points given and the gradient 2, I found that it goes through -2.
Then I put this information into the form y=mx + c and got y=2x-2

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- Loser66

Mistake: the given line has slope m= -2/3, not 2

- anonymous

ooooooh

- Loser66

Take my trick, ok?

- anonymous

ok?

- Loser66

|dw:1441024109280:dw|

- anonymous

Oh wow. Well that just made everything like 10 times easier.

- anonymous

One last thing though...

- Loser66

Notes: For parallel lines only.

- anonymous

In some of the answer to this type of equation they rearrange it (to give it in the kind of form as 2x + 3y=10 ) and sometimes they dont. For example: say I just found the equation of a line and it is y=-1/5x-1 , how do I know if thats the answer or if it needs to be rerranged to give x+5y+5=0 ?

- anonymous

Ok, noted. Thanks

- Loser66

In this case, you move x, y to one side, number in other side, then you get the right form to apply.

- anonymous

Ok, must I always do that?

- Loser66

it is not a must, but it makes the stuff easier.

- anonymous

The only thing I am concerned about is that I am trying to do that where it can't be done. A couple times I tried to do that and then gave it in the wrong form because of it.

- anonymous

I mean, one of the answers was in the original form of y=mx +c (it was y=3x-14) so they didn't do it then. Why are they doing it for some and not for others?

- Loser66

Give me the whole thing, I will work it in neat for you as an example

- anonymous

Thank you so much, ok...

- anonymous

parallel to 3x - y - 1=0 and passing through (4,-2)

- Loser66

hey, it is easy, just move x, y to one side and number to another side
3x - y =1
then replace the point in ( ignore the right hand side)
3*(4) - (-2) = 14
hence the required line is 3x -y = 14
then move back to original form 3x -y -14 =0

- anonymous

Ok, thank you very much! I think I understand now, that has helped me rather a lot. Have a nice day!

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