little question

Discussion in 'Physics & Math' started by qfrontier, Sep 7, 2002.

  1. qfrontier Captain Of Starship Registered Senior Member

    Messages:
    114
    how do you find the equation of this line;

    Slope=3
    Y-Intercept=2

    Using the Ax+By+C=0 method? and what does Ax, By and C suppose to mean?

    Thanks for any help!

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  3. Emfuser Registered Senior Member

    Messages:
    90
    If you're defining a line on a regular x-y plane, you can make the line equation a function of one variable (x or y).

    For slope=3, Y-Intercept=2, the basic equation (y=mx + b) is merely a reduction of your equation with the assumption that B=1. Thus Ax + By + C = 0 becomes -3x +y -2 = 0 and can be written as y = 3x + 2 . If B != 1, then you end up with y=(3x+2)/B.

    That's my educated guess.
     
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  5. qfrontier Captain Of Starship Registered Senior Member

    Messages:
    114
    is the y=mx+b form the same as Ax+By+C=0 form?
     
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  7. Emfuser Registered Senior Member

    Messages:
    90
    It is for all I can see. If you want to define y in terms of x, then you substitute A for m and C for b s.t. y=(Ax + C)/B = (mx + b)/B

    The only thing about the generic y = mx + b equation that excludes the B term is an assumption that B is one or has already been divided into A & C.
     
  8. HallsofIvy Registered Senior Member

    Messages:
    307
    Actually, there is an important difference between "Ax+ By+ C=0" form and "y= mx+ b". The second form cannot be used to represent a vertical line (x= 2 for example) while the first can. (It would be x-2= 0 with A= 1, B=0, C= -2.
     
  9. James R Just this guy, you know? Staff Member

    Messages:
    37,110
    qfrontier,

    You problem is to relate the undermined coefficients A, B and C to the slope and intercept.

    Let's look at the equation:

    Ax + By + C = 0

    The y intercept is where x=0, so

    By<sub>intercept</sub> + C = 0 --- (1)

    The slope we get from rearranging the equation:

    By = -Ax - C

    y = -(A/B)x - (C/B)

    This is in the form y = mx + c, where

    m = -(A/B) and c = -(C/B)

    m is the slope, and c is the y intercept. Notice that if we rearrange equation (1) we get y<sub>intercept</sub> = -C/B, which agrees with this.

    You are given that

    Slope=3
    Y-Intercept=2

    so

    -C/B = 2
    -A/B = 3

    We have two equations and three variables, so we can set one of the variables arbitrarily. Let's choose B=1 for simplicity. Then:

    C = -2 and A = -3

    The equation you want is:

    -3x + y - 2 = 0

    or y = 3x + 2
     

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