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Thread: Am I graphing this equation correctly?

  1. #1
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    Am I graphing this equation correctly?

    Hello everyone!
    I'm not sure if I'm doing this right. My instructions were to "Graph the given equations:"

    $\displaystyle \frac{y}{3}-\frac{x}{6} = -2 $

    I'm using these numbers for x.
    -2, -1, 0, 1, 2

    This is what I've been doing:

    (1) $\displaystyle \frac{y}{3}-\frac{-2}{6} = -2 $

    (2)Use LCD to get rid of fraction? *
    I used: $\displaystyle \frac{3}{1}$ on both sides. then I got:
    $\displaystyle y - \frac{-2}{2} = -6$

    (3)$\displaystyle y - (-1) = -6$ *

    (4)Then I added -1 to both sides.
    $\displaystyle y = -7$

    So that means my first point would be:
    $\displaystyle (-2,-7)$

    Then when I try to do it when $\displaystyle x = -1$
    I get $\displaystyle y = -2$

    With x = -1, I think I mess up on step 4.
    $\displaystyle y - \frac{-1}{2} = - 6$

    I subtract both sides with $\displaystyle \frac{-1}{2}$
    And I keep getting $\displaystyle y = -2$

    Help please and thanks in advance.

    * = Not sure about this step.
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Somatic View Post
    Hello everyone!
    I'm not sure if I'm doing this right. My instructions were to "Graph the given equations:"

    $\displaystyle \frac{y}{3}-\frac{x}{6} = -2 $

    I'm using these numbers for x.
    -2, -1, 0, 1, 2

    This is what I've been doing:

    (1) $\displaystyle \frac{y}{3}-\frac{-2}{6} = -2 $

    (2)Use LCD to get rid of fraction? *
    I used: $\displaystyle \frac{3}{1}$ on both sides. then I got:
    $\displaystyle y - \frac{-2}{2} = -6$

    (3)$\displaystyle y - (-1) = -6$ *

    (4)Then I added -1 to both sides.
    $\displaystyle y = -7$

    So that means my first point would be:
    $\displaystyle (-2,-7)$

    Then when I try to do it when $\displaystyle x = -1$
    I get $\displaystyle y = -2$

    With x = -1, I think I mess up on step 4.
    $\displaystyle y - \frac{-1}{2} = - 6$

    I subtract both sides with $\displaystyle \frac{-1}{2}$
    And I keep getting $\displaystyle y = -2$

    Help please and thanks in advance.

    * = Not sure about this step.
    Convert the equation into the form $\displaystyle y=mx+c$

    $\displaystyle
    \frac{y}{3}-\frac{x}{6} = -2
    $

    $\displaystyle \frac{y}{3} = -2 + \frac{x}{6}$

    Multiply by 3:

    $\displaystyle y = \frac{x}{2} - 6 = \frac{x-12}{2}$

    Now is should be easier to see that $\displaystyle f(-1)$ is $\displaystyle -\frac{13}{2}$ and $\displaystyle f(-2) = -7$
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