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Math Help - Simple eqN of a line question

  1. #1
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    Simple eqN of a line question

    Hey,

    I have this question thats been bugging me for a few days now.

    3y-15=2x-8

    Whats the answer if we put it in the eqN of a line?

    2x-3y+7=0 OR 2x-3y-7=0?

    Thanks for the help.
    -NZF
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by 905
    Hey,

    I have this question thats been bugging me for a few days now.

    3y-15=2x-8

    Whats the answer (below) if we put it in the eqN of a line?

    2x-3y+7=0 or 2x-3y-7=0?

    Thanks for the help.
    -NZF
    are you asking the solution of the line (when y equals 0) or are you asking for us to put the equation in standard/y-intercept/point-slope form?
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  3. #3
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    Quote Originally Posted by Quick
    are you asking the solution of the line (when y equals 0) or are you asking for us to put the equation in standard/y-intercept/point-slope form?
    Put the equation in standard form.

    EDIT: Actually it's just part of a question, the only part I don't fully understand.

    -NZF
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  4. #4
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by NineZeroFive
    Put the equation in standard form.
    alright, standard form is in the form of ax+by=c therefore we start with your equation...

    3y-15=2x-8

    add 15 to both sides 3y=2x-8+15

    subtract 2x from both sides: 3y-2x=7

    voila!

    ~ Q\!u\!i\!c\!k
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by NineZeroFive
    Hey,

    I have this question thats been bugging me for a few days now.

    3y-15=2x-8

    Whats the answer if we put it in the eqN of a line?

    2x-3y+7=0 OR 2x-3y-7=0?

    Thanks for the help.
    -NZF
    Algebraically it would have to be 2x-3y+7=0. Other standard forms:
    y = \frac{2}{3}x + \frac{7}{3} (Slope - Intercept form)

    and

    (y - 3) = \frac{2}{3}(x - 1) (An example of point-slope form)

    and

    \frac{x}{3} - \frac{y}{2} = - \frac{7}{6} (I forget what this one is called.)

    -Dan
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  6. #6
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    Quote Originally Posted by Quick
    alright, standard form is in the form of ax+by=c therefore we start with your equation...

    3y-15=2x-8

    add 15 to both sides 3y=2x-8+15

    subtract 2x from both sides: 3y-2x=7

    voila!

    ~ Q\!u\!i\!c\!k
    3y-2x-7=0? Because it the textbook it says its 2x-3y+7=0?

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  7. #7
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by NineZeroFive
    3y-2x-7=0? Because it the textbook it says its 2x-3y+7=0?

    multiply both sides of 3y-2x-7=0 by negative 1
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  8. #8
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    Sorry,

    I think I made a typo somewhere.

    3y-15=2x-8 is the equation you need to put in the standard form.

    Is the answer 2x-3y+7=0? (textbook answer) Why? -.-

    Why is it NOT 2x-3y-7=0?

    -NZF
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  9. #9
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by NineZeroFive
    3y - 15 = 2x - 8
    3y - 15 = 2x - 8

    3y - 15 - 3y = 2x - 8 - 3y

    -15 = 2x - 3y - 8

    -15 + 15 = 2x - 3y - 8 + 15

    0 = 2x - 3y + 7

    -Dan
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  10. #10
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by NineZeroFive
    Sorry,

    I think I made a typo somewhere.

    3y-15=2x-8 is the equation you need to put in the standard form.

    Is the answer 2x-3y+7=0? (textbook answer) Why? -.-

    Why is it NOT 2x-3y-7=0?

    -NZF
    I assume you mean:
    Quote Originally Posted by NineZeroFive
    Sorry,

    I think I made a typo somewhere.

    3y-15=2x-8 is the equation you need to put in the standard form.

    Is the answer 2x-3y+7=0? (textbook answer) Why? -.-

    Why is it NOT 3y-2x-7=0?

    -NZF
    but the answer, both equations are correct, your book is just picky.
    although I must say, I've never actually seen standard form equalling zero...
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  11. #11
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick
    I assume you mean:


    but the answer, both equations are correct, your book is just picky.
    although I must say, I've never actually seen standard form equalling zero...
    One standard way of writing a multinomial (the "most" standard I've seen, if there is such a thing) is to write the terms of highest degree first down to the lowest degree such that the expression equals zero. For example:
    3x^2y^3 - xy^2 + 12x - 3y + 5 = 0

    In the case for a linear equation the form simply becomes:
    ax + by + c = 0

    I'll admit I don't usually see this form for a line, but considering the expression as a multinomial it would be standard.

    -Dan
    Last edited by topsquark; July 30th 2006 at 04:09 PM. Reason: PS
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  12. #12
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    Quote Originally Posted by Quick
    I assume you mean:


    but the answer, both equations are correct, your book is just picky.
    although I must say, I've never actually seen standard form equalling zero...
    I'm still kinda confused because the book says "The equation of the line through A and B is 2x-3y+7=0.

    Why is it 2x-3y+7=0 and NOT 2x-3y-7=0?

    hmm..

    -NZF
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  13. #13
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by NineZeroFive
    I'm still kinda confused because the book says "The equation of the line through A and B is 2x-3y+7=0.

    Why is it 2x-3y+7=0 and NOT 2x-3y-7=0?

    hmm..

    -NZF
    Unless you have a question about my derivation, please see post #9 under this thread. I derived the form there.

    -Dan
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