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Write y as a function of x

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    • Thread Starter

    Given the equation: 2x - 3y = 6

    Write y as a function of x.

    I know this is straightforward, and I have the line-by-line answer, but I can't understand how you get from:

    (2x - 3y = 6)
    - 3y = - 2x + 6 (So here you have shifted the 2x over as you want ultimately just y on the left)
    y = 2x/3 - 2 (Where's the -3? Why is there a fraction on the right? What's happened to the +6?)


    You divided both sides by -3.

    \frac{-3y}{-3} = y

    \frac{-2x}{-3} = \frac{2x}{3}

    \frac{6}{-3} = -\frac{6}{3} = -2.
    • Thread Starter

    Oh so you do it to the +6 AND the -2x. Got ya!
    • Thread Starter

    How would I then find the "intercept" and the "root"?

    The root is basically the value of x for which y = 0. So set y to and solve for x.

    The y-intercept is the value of y for which x = 0. So set x to 0 and solve for y.

    (Original post by tymbnuip)
    Oh so you do it to the +6 AND the -2x. Got ya!
    Yes you're "doing it" to the sides of the equation rather than the actual terms (at least that's one way of looking at it).

    If you didn't, your equation would not hold. There's only a limited number of valid operations you can do to an equation (an equation states that something on the left side is equal to something on the right side) like add/subtract a number to each side or multiply the left expression and the right expression by the same factor (in your case that factor is -3)
    • Thread Starter

    The root (x -intercept) is when y = 0

    2x/3 - 2 = 0

    2x - 6 = 0 {multiply both sides by 3}
    So how does the /3 disappear by multiplying by 3? Wouldn't it turn into 9?

    (Original post by tymbnuip)
    So how does the /3 disappear by multiplying by 3? Wouldn't it turn into 9?
    \frac{2x}{3} - 2 = 0

    \frac{2x}{3} . \frac{3}{1} - 2 . \frac{3}{1} = 0 . \frac{3}{1}

    2x - 6 = 0

    When multiplying two fractions, multiply the top by the top and the bottom by the bottom

    2x times 3 = 6x

    3 times 1 = 3

    6x/3 = 2x

    Get it?
    • Thread Starter

    What does the =0.3/1 mean?

    Urgh sorry

    it means 0 times \frac{3}{1}
    • Thread Starter

    Heh okay. So I guess now I have 2x - 6 = 0 I want to get rid of the 6?


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