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Different forms of linear equations

  1. Apr 15, 2006 #1
    A while back in maths we were introduced to the linear equation in two forms:

    [tex]a x + b y = c[/tex] (1)

    [tex]y = m x + c[/tex] (2)

    Now I can use both forms of these, but I was told that:

    [tex] y = m x + c \Leftrightarrow a x + b y = c [/tex]

    where [tex]m = \frac{a}{b} [/tex]

    Thiis can't be right can it? As:

    [tex]a x + b y = c [/tex]

    [tex] b y = c - a x [/tex]

    [tex] y = \frac{c}{b} - \frac{a x }{b}[/tex]
     
    Last edited: Apr 15, 2006
  2. jcsd
  3. Apr 15, 2006 #2

    Astronuc

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    Staff: Mentor

    Obviously the c's in equations 1 and 2 are not the same. They cannot be as you have demonstrated.

    Using [tex] y = \frac{c}{b} - \frac{a x }{b}[/tex]

    and [tex]y = m x + d[/tex],

    then m = [tex]-\frac{a}{b}[/tex] and

    d = [tex]\frac{c}{b}[/tex]
     
  4. Apr 15, 2006 #3
    Thanks. My teacher was saying the two forms are the same (ie: at least "c" in both equations are the same). I couldn't prove it, and nor could she, and we both forgot about it.
     
  5. Apr 15, 2006 #4

    Astronuc

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    Staff: Mentor

    Both equations represent a line, but the coefficients must be numerically different.

    Basically, one is dividing all terms in (1) by the coefficient (b) of y, and to be equal, the m = - (a/b) and c in equation 2 must be c/a, so the c's must be different.
     
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