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Math Help - Solving a Slope-Intercept Form Equation Help?

  1. #1
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    Solving a Slope-Intercept Form Equation Help?

    Hello everyone, I have a small issue while solving an equation in the form of slope-intercept, they give me an equation and ask me to solve it and graph it.

    Formula Given for Graphing: y=mx+b

    Equation: -3x - 6y = 12

    So I know I have to solve for y, so here's what I do:

    add -3x to 12, and that's where I get lost. I saw a video on youtube that said when you do that, you don't really add the -3x to 12, it just becomes the slope in the next step so for example it would be: -6y=-3x + b? Not sure if that's right.

    Help is appreciated, thanks.
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  2. #2
    Super Member Quacky's Avatar
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    Re: Solving a Slope-Intercept Form Equation Help?

    Not quite.

    -3x-6y=12

    Adding 3x to both sides:

    -3x+3x-6y=12+3x

    -6y=12+3x

    So how would you finish?
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  3. #3
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    Re: Solving a Slope-Intercept Form Equation Help?

    Can it be done like this?

    -3x -6y = 12

    add 3x to both sides, and it becomes:

    -6y= 3x + 12

    divide by -6:

    y=-3x/-6 + 12/-6

    y= y = -1/2 x - 2?

    Assuming that's right, what it is, is that whatever your first step is becomes the slope, then to leave y by itself, you divide everything, but ONLY simplify the slope?
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  4. #4
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    Re: Solving a Slope-Intercept Form Equation Help?

    Quote Originally Posted by Iceycold View Post
    Can it be done like this?

    -3x -6y = 12

    add 3x to both sides, and it becomes:

    -6y= 3x + 12

    divide by -6:

    y=-3x/-6 + 12/-6

    y= y = -1/2 x - 2?

    Assuming that's right, what it is, is that whatever your first step is becomes the slope, then to leave y by itself, you divide everything, but ONLY simplify the slope?
    Be careful with your signs. Since you added 3x to both sides, the 3 should be positive.

    You are correct with y = \frac{-1}{2}x - 2

    But I don't agree with the last part. Questions won't always just be dealing with the slope. There will be times when you need to know things about the intercepts or equation in general, so simplify where possible, unless asked otherwise.
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  5. #5
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    Re: Solving a Slope-Intercept Form Equation Help?

    Yeah sorry, that might of been confusing, thanks! Sigh, you explained this way better than my algebra teacher in under 20 minutes.

    edit: in the case that the initial -3x, wasn't negative and it was positive, the first step would be:

    3x - 6y = 12 ---> -6y = 3x - 12? or is it -3x - 12?
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  6. #6
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    Re: Solving a Slope-Intercept Form Equation Help?

    If it had been 3x-6y=12, instead of adding 3x to both sides, you'd need to subtract 3x from both sides.

    3x - 6y = 12

    3x - 3x - 6y = 12 - 3x

    -6y=12-3x

    Alternatively, you could add 6y to both sides.

    3x - 6y = 12

    3x - 6y + 6y = 12 + 6y

    3x=12+6y

    And then subtract 12 from both sides.

    3x-12=6y
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  7. #7
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    Re: Solving a Slope-Intercept Form Equation Help?

    But in slope intercept form, doesn't B (12) have to be on the right side? example: y=mx+(12)

    So I'm assuming it'll be -6y=3x-12?
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  8. #8
    Super Member Quacky's Avatar
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    Re: Solving a Slope-Intercept Form Equation Help?

    mx+c=y is the same as y=mx+c

    Edit: In your answer, you might write it as y=\cdots for clarity, though.
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  9. #9
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    Re: Solving a Slope-Intercept Form Equation Help?

    Right. -6y = 3x - 12 = -6y = 12 - 3x. Gotcha, thanks!
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  10. #10
    Super Member Quacky's Avatar
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    Re: Solving a Slope-Intercept Form Equation Help?

    Ahhhhh! Be careful!

    Don't change the signs of things!

    -6y = 3x - 12 = -6y = -12 + 3x
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  11. #11
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    Re: Solving a Slope-Intercept Form Equation Help?

    Ah, yes, how bad of me hehe, well thanks for all the help got it now.

    edit: Just to solve it,

    3x - 6y = 12

    subtract -3x

    -6y = 12 - 3x

    divide by -6

    y = 12/-6 - -3x/-6

    y = -2 - 1/2

    A graphing would look like: start at -2 for the y-intercept, then go down -1, and run over 2 spaces?

    edit: Also since I'm more used to reading y=mx + b than reading y=b + mx, how can I write this: -6y = 12 - 3x in the y=mx+b form, I know it's the same but just to make it easier on me.
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  12. #12
    Super Member Quacky's Avatar
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    Re: Solving a Slope-Intercept Form Equation Help?

    -6y=-3x+12

    Addition is commutative: the order in which things are added doesn't matter. To graph y=\frac{-1}{2}x-2, set x=0, and deduce that y=-2, then set y=0 and deduce that x=-4

    You now have 2 points, (-4, 0) and (0,-2) and you can just draw the line connecting these points. You could think of it as going down 1 space, and horizontally right 2 spaces.

    Edit: Corrected a typo.
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  13. #13
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    Re: Solving a Slope-Intercept Form Equation Help?

    Alright, got it.

    And just to make sure since I always write the equation on paper as y=mx + b, where the y intercept is always on the right, the addition between the mx and b never changes right? what changes is whether the mx is positive or negative right?
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  14. #14
    Super Member Quacky's Avatar
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    Re: Solving a Slope-Intercept Form Equation Help?

    Not sure I understand the question, but I think so.

    Why not check by trying another example:

    How would you write:

    3-4y=8x

    In y=mx+c form?
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  15. #15
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    Re: Solving a Slope-Intercept Form Equation Help?

    What I meant was, the equation made after the first step to solving it in y=mx+b form will always be mx will either be negative or positive depending on the initial equation, and the + b will always remain right?

    edit: let me clarify, b will ALWAYS be positive, then mx can be either positive or negative? So an equation for me would always be written y= mx (can be negative or positive) then + b?

    That equation you posted in y=mx+b form would be: -4y= 8x + 3.
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